This analysis was prepared by Francisco Arrieta and Jonathan Edwards.

1 Setup

# options(scipen=999) #prevent scientific notation
# options(scipen=-999) #encourage scientific notation
options(scipen=0) #encourage scientific notation neutral?
# kable table layout options
# do not display NAs and only 2 digits
opts <- options(knitr.kable.NA = '') #knitr.table.format = "latex"

# define table styling options
stable <- function(data, digits = 2) {
  knitr::kable(data, digits=digits) |> 
    # kable_styling(c("striped", "condensed"))
    kable_paper(full_width = F)
}

1.1 libraries

# modelling
library(psych) #factor analysis tools (PAF PAF)
library(lavaan) #causal analysis
library(lm.beta) # add standarized regression coeffs

# stats
library(nortest) #Kolmogorov-Smirnov-Test
library(corrplot) #correlation matrix plot
library(olsrr)  #VIF and Tolerance Values
library(pastecs) # provides function stat.desc
library(REdaS) #Bartelett's Test

# plotting & formatting
library(ggplot2) #better graphs
library(patchwork) # provides wrap_plots for multiplotting 
# library(gridExtra) #provides multiplotting functionality
# library(ggpubr) #provides ggarrange for multiplotting (patchwork better though)
library(semPlot) #for visualization of path diagrams (SEM)
library(lavaanPlot) #for visualization of path diagrams (SEM)
# library(rcompanion)   #Histogram and Normal Curve
library(kableExtra) #makes nice tables

# generic
library(dplyr) #useful data manip functions like arrange, distinct, rename etc included in fpp3
library(stringr) # provides string manip functions like str_split_fixed 
library(Hmisc) #describe function that describes features of dataframes
library(data.table) # creating and manipulating datatables
library(knitr) #rmarkdown tools not sure why useful
library(parameters) #get model outputs in table form (good for making tabs)

1.2 Load data

survey <- read.csv("Case Study III_Structural Equation Modeling.csv")
labels <- read.csv("Variables and Labels_Galeries Lafayette.csv")

dim(survey)
## [1] 553  45
# head(labels)

1.3 labels

#Make labels more readable
#create copy of label column without variable code
labels["Category"] <- sub("[^-]*\\s-","",labels[["Label"]]) 
# labels["Category"] <- sub(".*\\s-","",labels[["Label"]])
# labels

#split this new column (category) into category and short label
labels[c("Category","Label_short")] <- str_split_fixed(labels[["Category"]],"\\?\\s\\s|\\s-", n=2)
# labels[20:25,c("Category","Label_short")]
labels[,c("Variable","Category","Label_short")] |>
  stable()
Variable Category Label_short
Im1 What do GLB represent from your point of view Large Assortment
Im2 What do GLB represent from your point of view Assortment Variety
Im3 What do GLB represent from your point of view Artistic Decoration of Sales Area
Im4 What do GLB represent from your point of view Creative Decoration of Sales Area
Im5 What do GLB represent from your point of view Appealing Arrangement of Shop Windows
Im6 What do GLB represent from your point of view France
Im7 What do GLB represent from your point of view French Savoir-vivre
Im8 What do GLB represent from your point of view Expertise in French Traditional Cuisine
Im9 What do GLB represent from your point of view French Fashion
Im10 What do GLB represent from your point of view Gourmet Food
Im11 What do GLB represent from your point of view High-quality Cosmetics
Im12 What do GLB represent from your point of view Luxury brands
Im13 What do GLB represent from your point of view Up tp date Designer Brands
Im14 What do GLB represent from your point of view Gourmet specialities
Im15 What do GLB represent from your point of view Professional Selection of Brands
Im16 What do GLB represent from your point of view Professional Appearance Towards Customers
Im17 What do GLB represent from your point of view Are Trendy
Im18 What do GLB represent from your point of view Are Hip
Im19 What do GLB represent from your point of view Professional Organization
Im20 What do GLB represent from your point of view Relaxing Shopping
Im21 What do GLB represent from your point of view A Great Place to Stroll
Im22 What do GLB represent from your point of view Intimate Shop Atmosphere
C_CR1 CO-CREATION I would like to participate in an expert-workshop to improve the assortment of Galeries Lafayette Berlin.
C_CR2 CO-CREATION I would be available to take part in another survey at Galeries Lafayette Berlin.
C_CR3 CO-CREATION I would like to become a member of a customer group whose opinion is obtained for new products and major changes.
C_CR4 CO-CREATION I would like to participate in planning and designing special events (e.g. fashion show, introduction of new car models) if asked.
C_REP1 REPURCHASE I will continue to be a loyal customer of Galeries Lafayette Berlin.
C_REP2 REPURCHASE I intend to shop at Galeries Lafayette Berlin in the future.
C_REP3 REPURCAHSE I will surely visit Galeries Lafayette Berlin in the future.
COM_A1 AFFECTIVE COMMITMENT How strongly are you attached to Galeries Lafayette Berlin?
COM_A2 AFFECTIVE COMMITMENT How strongly are you emotionally connected to Galeries Lafayette Berlin?
COM_A3 AFFECTIVE COMMITMENT As a customer I feel (close) attached to GL
COM_A4 AFFECTIVE COMMITMENT feel a strong emotional bond toward GLB
SAT_1 SATISFACTION I am very satisfied with Galeries Lafayette Berlin.
SAT_2 SATISFACTION Overall, I am very satisfied with Galeries Lafayette Berlin.
SAT_3 SATISFACTION How satisfied are you with Galeries Lafayette Berlin?
SAT_P1 SATISFACTION EMPLOYEES The employees are capable and professional.
SAT_P2 SATISFACTION EMPLOYEES The employees know best about their products.
SAT_P3 SATISFACTION EMPLOYEES The employees are well-informed.
SAT_P4 SATISFACTION EMPLOYEES The employees are always helpful.
SAT_P5 SATISFACTION EMPLOYEES The employees are willing to respond to my questions in detail.
SAT_P6 SATISFACTION EMPLOYEES The employees are friendly.
TRU_1 TRUST I have the feeling that I can completely rely on GL.
TRU_2 TRUST GLB will always be honest and trustful with me.
TRU_3 TRUST GL will treat me always fair as a customer

1.4 Clean and handle missing data

# # omit all unanswered
# filter_all(survey, all_vars(. != 999))
# filter_all(survey, any_vars(. %in% c(999)))
# 
# filter_all(select(survey,1:22,"SAT_1"), all_vars(. != 999))
# filter_all(select(survey,1:22,"SAT_1"), any_vars(. %in% c(999)))
# 
# filter_all(data_img_EFA, all_vars(. != 999))
# filter_all(ges, any_vars(. %in% c(999)))
# delete variables unused in analysis (see case study instructions): 
survey <- survey |> select(-c("C_CR2", "SAT_P1", "SAT_P2", "SAT_P3", "SAT_P4", "SAT_P5", "SAT_P6", "TRU_1", "TRU_2", "TRU_3"))

# replace missing data (999) with NA
survey <- data.frame(sapply(survey,function(x) ifelse((x==999),NA,as.numeric(x))))

1.5 Explore Data

2 Dimensions by which Galeries Lafayette is perceived

2.1 ROUND 1: Exploratory factor analysis

2.1.1 Variable selection for EFA

# excluded image variables (in the first round of EFA we don't exclude any image variables...)
exclude=c() 

# the full survey data (includes dependent and independent variables) with excluded image variables (in this first round of EFA we don't exclude anything)
survey_excl_img <- survey |> select(-exclude)

# the data we will use for EFA (images)
data_img_EFA <- survey_excl_img[1:(22-length(exclude))]

2.1.2 handle missing data

# delete missing data (delete listwise)
data_img_EFA <- na.omit(data_img_EFA)

dim(survey)
## [1] 553  35
dim(survey_excl_img)
## [1] 553  35
dim(data_img_EFA)
## [1] 385  22

2.1.3 Check adequacy of correlation Matrix

2.1.3.1 correlation matrix

#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA)
corrplot(as.matrix(corr_matrix), 
         method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
         order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
         addCoef.col = 'black', number.cex = .5,
         tl.col ="black", 
         tl.cex = 0.80, 
         )

Variables to look out for going forward:

  • Images 9 and 11 are alone

  • Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).

2.1.3.2 Bartlett’s Test

bart_spher(data_img_EFA)
##  Bartlett's Test of Sphericity
## 
## Call: bart_spher(x = data_img_EFA)
## 
##      X2 = 6451.238
##      df = 231
## p-value < 2.22e-16

The Bartlett Test tests the hypothesis that the sample originates from a population, where all variables are uncorrelated. This would not be good for factor analysis, we want this hypothesis to be rejected meaning p-value < 5%.

In our case we see that it is indeed rejected and that the data is not uncorrelated.

2.1.3.3 KMO

KMOTEST=KMOS(data_img_EFA)
print(KMOTEST, sort=T)
## 
## Kaiser-Meyer-Olkin Statistics
## 
## Call: KMOS(x = data_img_EFA)
## 
## Measures of Sampling Adequacy (MSA):
##       Im2       Im6       Im1      Im20      Im14      Im10       Im7       Im4 
## 0.8224640 0.8224827 0.8244624 0.8266391 0.8267452 0.8285789 0.8448231 0.8542604 
##      Im18       Im3      Im17      Im13      Im12      Im22      Im16      Im11 
## 0.8550678 0.8640362 0.8644991 0.8722220 0.8789413 0.8793157 0.9092200 0.9113882 
##      Im21       Im8       Im9      Im19       Im5      Im15 
## 0.9149654 0.9300079 0.9380091 0.9400714 0.9546668 0.9647563 
## 
## KMO-Criterion: 0.8770975

The KMO of 0.8770975 is above 0.6 which indicates the data is well suited for factor anlysis.

2.1.3.4 Anti-image Correlation

MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))

# Sort table
MSA_list<- MSA_list |> 
  setorder(cols = "MSA")

# Display table
MSA_list |> 
  stable() |>
  row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")
Item MSA
Im2 0.82
Im6 0.82
Im1 0.82
Im20 0.83
Im14 0.83
Im10 0.83
Im7 0.84
Im4 0.85
Im18 0.86
Im3 0.86
Im17 0.86
Im13 0.87
Im12 0.88
Im22 0.88
Im16 0.91
Im11 0.91
Im21 0.91
Im8 0.93
Im9 0.94
Im19 0.94
Im5 0.95
Im15 0.96

Variables with MSA values above 0.5 are suited for factor analysis. Presence of items with low MSA’s (<0.5) could also indicate that an important topic hasn’t been well covered in the questionnaire.

All variables have MSA above 0.5

2.1.4 Select method: PAF

2.1.4.1 Extract factors

EFA_PAF0 <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified
2.1.4.1.1 Scree plot
#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
     ylab="Eigenvalue",
     main="Scree plot",
     cex.lab=1.2,
     cex.axis=1.2,
     cex.main=1.8,
     col = "#0099F8",
     pch = 19) 
abline(h=1, col = "#7F35B2")

2.1.4.1.2 Kaiser Criterion
EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb
## [1] 6

The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.

There are 6 factors satisfying this condition.

2.1.4.1.3 Total Variance Explained
#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
                                            seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
                                          EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
                                          Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
                                          Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |> 
  stable()
Factor number EigenValue Variance Total_Variance
1 8.98 40.81 0.41
2 2.47 11.21 0.52
3 1.56 7.10 0.59
4 1.46 6.62 0.66
5 1.25 5.67 0.71
6 1.15 5.22 0.77
7 0.81 3.68 0.80
8 0.71 3.23 0.84
9 0.57 2.58 0.86
10 0.46 2.08 0.88
11 0.36 1.64 0.90
12 0.33 1.51 0.91
13 0.29 1.34 0.93
14 0.28 1.29 0.94
15 0.25 1.13 0.95
16 0.23 1.04 0.96
17 0.20 0.92 0.97
18 0.19 0.85 0.98
19 0.16 0.72 0.99
20 0.12 0.53 0.99
21 0.10 0.46 1.00
22 0.08 0.37 1.00

With 6 factors we would explain 76.6310791% of total variance.

With 7 factors we would explain 80.3133487% of total variance.

# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue
## [1] 8.377985

2.1.4.2 Determine number of factors to retain

# select nb of factors to test
nf = c(5,6,7,8)

2.1.4.3 PAF orthogonal Varimax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()

i=1
for (n in nf) {
  # EFA_PAFn[[i]] <- n
  EFA_PAFn[[i]] <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn) <- nf
2.1.4.3.1 Communalities
#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
    EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn[[i]]$communality))

    # Sort table
    EFA_PAFn_communalities <- EFA_PAFn_communalities |>
      setorder(cols = "Communality")
    
    # Display table
    kbl <- EFA_PAFn_communalities |> 
              stable() |>
              row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn[[i]]$loadings["Im9",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im9 =", communality))
    cat("\n")
    
}
Number of factors = 5
Item Communality
Im9 0.41
Im11 0.41
Im18 0.43
Im16 0.46
Im6 0.50
Im19 0.53
Im17 0.54
Im5 0.55
Im15 0.63
Im21 0.65
Im14 0.66
Im10 0.66
Im7 0.69
Im20 0.69
Im12 0.71
Im13 0.72
Im2 0.76
Im8 0.76
Im22 0.81
Im1 0.82
Im3 0.86
Im4 0.92

[1] “Communality for Im9 =0.405600881872799”

Number of factors = 6
Item Communality
Im11 0.45
Im9 0.46
Im16 0.47
Im19 0.52
Im5 0.55
Im18 0.57
Im15 0.63
Im21 0.65
Im17 0.70
Im13 0.70
Im6 0.71
Im12 0.73
Im8 0.74
Im14 0.76
Im2 0.76
Im10 0.78
Im7 0.78
Im20 0.79
Im22 0.79
Im1 0.84
Im3 0.85
Im4 0.92

[1] “Communality for Im9 =0.463399199002637”

Number of factors = 7
Item Communality
Im11 0.44
Im9 0.46
Im16 0.47
Im19 0.53
Im5 0.54
Im15 0.63
Im21 0.65
Im13 0.70
Im18 0.71
Im8 0.72
Im6 0.76
Im2 0.78
Im22 0.79
Im20 0.79
Im14 0.81
Im12 0.83
Im7 0.85
Im1 0.86
Im3 0.86
Im10 0.89
Im17 0.95
Im4 0.97

[1] “Communality for Im9 =0.455673655610471”

Number of factors = 8
Item Communality
Im11 0.45
Im9 0.46
Im5 0.58
Im19 0.62
Im15 0.65
Im21 0.65
Im13 0.70
Im8 0.72
Im18 0.74
Im6 0.76
Im22 0.78
Im16 0.80
Im2 0.81
Im20 0.81
Im12 0.84
Im7 0.85
Im14 0.85
Im3 0.86
Im10 0.90
Im17 0.93
Im1 0.94
Im4 0.97

[1] “Communality for Im9 =0.455554069181416”

Typically we should think about excluding variables with communalities below 0.3.

Based on the above, no variable should be excluded.

2.1.4.3.2 Factor loadings
# loadings for all selected number of factors

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
      
cat("\n\n")
}
Number of factors = 5
Variable MR2 MR5 MR4 MR1 MR3 Complexity Uniqueness
Im1 0.85 1.31 0.18
Im2 0.83 1.23 0.24
Im3 0.83 1.55 0.14
Im4 0.87 1.46 0.08
Im5 0.64 1.78 0.45
Im6 0.67 1.22 0.50
Im7 0.79 1.20 0.31
Im8 0.84 1.16 0.24
Im9 0.43 0.39 2.76 0.59
Im10 0.75 1.37 0.34
Im11 0.57 1.56 0.59
Im12 0.79 1.27 0.29
Im13 0.77 1.43 0.28
Im14 0.75 1.37 0.34
Im15 0.60 0.33 2.66 0.37
Im16 0.48 0.37 2.77 0.54
Im17 0.38 0.48 3.44 0.46
Im18 0.31 0.43 3.42 0.57
Im19 0.47 0.40 3.37 0.47
Im20 0.78 1.27 0.31
Im21 0.74 1.41 0.35
Im22 0.81 1.51 0.19
Number of factors = 6
Variable MR2 MR5 MR1 MR4 MR3 MR6 Complexity Uniqueness
Im1 0.86 1.30 0.16
Im2 0.83 1.24 0.24
Im3 0.83 1.51 0.15
Im4 0.88 1.42 0.08
Im5 0.64 1.74 0.45
Im6 0.61 0.56 2.12 0.29
Im7 0.72 0.48 1.88 0.22
Im8 0.81 1.25 0.26
Im9 0.35 0.32 0.43 3.51 0.54
Im10 0.80 1.42 0.22
Im11 0.59 1.62 0.55
Im12 0.79 1.34 0.27
Im13 0.73 1.66 0.30
Im14 0.80 1.42 0.24
Im15 0.60 2.76 0.37
Im16 0.48 0.37 2.78 0.53
Im17 0.35 0.31 0.39 0.54 3.66 0.30
Im18 0.35 0.50 3.48 0.43
Im19 0.46 0.40 3.45 0.48
Im20 0.84 1.22 0.21
Im21 0.73 1.43 0.35
Im22 0.79 1.60 0.21
Number of factors = 7
Variable MR5 MR1 MR3 MR2 MR4 MR7 MR6 Complexity Uniqueness
Im1 0.86 1.33 0.14
Im2 0.83 1.27 0.22
Im3 0.83 1.56 0.14
Im4 0.90 1.40 0.03
Im5 0.63 1.85 0.46
Im6 0.83 1.25 0.24
Im7 0.32 0.84 1.44 0.15
Im8 0.63 0.51 2.31 0.28
Im9 0.33 0.45 3.45 0.54
Im10 0.87 1.35 0.11
Im11 0.58 1.72 0.56
Im12 0.85 1.30 0.17
Im13 0.72 1.81 0.30
Im14 0.81 1.50 0.19
Im15 0.59 2.97 0.37
Im16 0.46 0.34 3.44 0.53
Im17 0.84 1.76 0.05
Im18 0.72 1.85 0.29
Im19 0.43 0.37 4.25 0.47
Im20 0.85 1.21 0.21
Im21 0.73 1.44 0.35
Im22 0.78 1.62 0.21
Number of factors = 8
Variable MR1 MR3 MR4 MR7 MR2 MR5 MR6 MR8 Complexity Uniqueness
Im1 0.88 1.45 0.06
Im2 0.82 1.45 0.19
Im3 0.81 1.66 0.14
Im4 0.89 1.47 0.03
Im5 0.65 1.84 0.42
Im6 0.83 1.23 0.24
Im7 0.84 0.30 1.40 0.15
Im8 0.54 0.59 2.56 0.28
Im9 0.33 0.46 3.34 0.54
Im10 0.87 1.41 0.10
Im11 0.58 1.72 0.55
Im12 0.86 1.28 0.16
Im13 0.72 1.78 0.30
Im14 0.83 1.49 0.15
Im15 0.47 0.39 4.81 0.35
Im16 0.77 1.78 0.20
Im17 0.82 1.82 0.07
Im18 0.74 1.76 0.26
Im19 0.30 0.54 3.68 0.38
Im20 0.86 1.20 0.19
Im21 0.73 1.44 0.35
Im22 0.78 1.63 0.22

Factor loadings:

  • Number of items per factor >=3
    • this condition is respected in all cases except when we have 8 factors. We eliminate the 8 factor solution
  • 0.40–0.30–0.20 rule: satisfactory variables (a) load onto their primary factor above 0.40, (b) load onto alter-native factors below 0.30, and (c) demonstrate a difference of 0.20 between their primary and alternative factor loadings.
    • 5 factor solution:
      • this condition is not respected for many variables. We eliminate the 5 factor solution
    • 6 factor solution:
      • this condition is not respected for: Im6, Im7, Im9, (Im11), (Im15), Im16, Im17, Im18, Im19 where Im17 and Im18 are particularly spread out
    • 7 factor solution:
      • this condition is not respected for: Im7, Im8, Im9, Im15, Im16, Im19 where Im16 and Im19 are particularly spread out

Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables.

Looking at the correlation matrix, we saw that variables Im16 and Im19 were highly correlated, we probably only need to exclude one of the two, Im19 has the lower communality of the two so we might consider eliminating that one.

Similarly Im17 and Im18 are highly correlated we might want to eliminate Im18 which has the lowest communality of the two, but they have adequately high loadings in the 7 factor solution so not a priority.

We might also exclude Im9 and Im15 as their communality is on the lower end and their loadings are spread out and quite weak. Also Im9 is problematic in both the 6 and 7 factor solution

Thurstone simple structure criteria:

  • Each row (variable) of the factor pattern matrix should have at least one zero

  • Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors

  • For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other

  • When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns

  • For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns

2.1.4.4 PAF oblique Promax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()

i=1
for (n in nf) {
  # EFA_PAFn_obl[[i]] <- n
  EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA, rotate="promax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn_obl) <- nf

length(EFA_PAFn_obl)
## [1] 4
2.1.4.4.1 Communalities
#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
    EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))

    # Sort table
    EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
      setorder(cols = "Communality")
    
    # Display table  
    kbl <- EFA_PAFn_obl_communalities |> 
              stable() |> 
              row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn_obl[[i]]$loadings["Im9",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im9 =", communality))
    cat("\n")
    
}
Number of factors = 5
Item Communality
Im9 0.41
Im11 0.41
Im18 0.43
Im16 0.46
Im6 0.50
Im19 0.53
Im17 0.54
Im5 0.55
Im15 0.63
Im21 0.65
Im14 0.66
Im10 0.66
Im7 0.69
Im20 0.69
Im12 0.71
Im13 0.72
Im2 0.76
Im8 0.76
Im22 0.81
Im1 0.82
Im3 0.86
Im4 0.92

[1] “Communality for Im9 =0.272947652560888”

Number of factors = 6
Item Communality
Im11 0.45
Im9 0.46
Im16 0.47
Im19 0.52
Im5 0.55
Im18 0.57
Im15 0.63
Im21 0.65
Im17 0.70
Im13 0.70
Im6 0.71
Im12 0.73
Im8 0.74
Im14 0.76
Im2 0.76
Im10 0.78
Im7 0.78
Im20 0.79
Im22 0.79
Im1 0.84
Im3 0.85
Im4 0.92

[1] “Communality for Im9 =0.339338697735652”

Number of factors = 7
Item Communality
Im11 0.44
Im9 0.46
Im16 0.47
Im19 0.53
Im5 0.54
Im15 0.63
Im21 0.65
Im13 0.70
Im18 0.71
Im8 0.72
Im6 0.76
Im2 0.78
Im22 0.79
Im20 0.79
Im14 0.81
Im12 0.83
Im7 0.85
Im1 0.86
Im3 0.86
Im10 0.89
Im17 0.95
Im4 0.97

[1] “Communality for Im9 =0.279736181915467”

Number of factors = 8
Item Communality
Im11 0.45
Im9 0.46
Im5 0.58
Im19 0.62
Im15 0.65
Im21 0.65
Im13 0.70
Im8 0.72
Im18 0.74
Im6 0.76
Im22 0.78
Im16 0.80
Im2 0.81
Im20 0.81
Im12 0.84
Im7 0.85
Im14 0.85
Im3 0.86
Im10 0.90
Im17 0.93
Im1 0.94
Im4 0.97

[1] “Communality for Im9 =0.302814913694533”

2.1.4.4.2 Factor loadings
# loadings for all selected number of factors

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
      
cat("\n\n")
}
Number of factors = 5
Variable MR2 MR5 MR1 MR4 MR3 Complexity Uniqueness
Im1 1.07 1.06 0.18
Im2 1.07 1.07 0.24
Im3 1.00 1.03 0.14
Im4 1.07 1.03 0.08
Im5 0.75 1.03 0.45
Im6 0.73 1.11 0.50
Im7 0.87 1.14 0.31
Im8 0.91 1.01 0.24
Im9 0.36 0.37 2.10 0.59
Im10 0.77 1.17 0.34
Im11 0.69 1.08 0.59
Im12 1.00 1.05 0.29
Im13 0.94 1.03 0.28
Im14 0.77 1.12 0.34
Im15 0.62 1.14 0.37
Im16 0.47 1.79 0.54
Im17 0.42 2.05 0.46
Im18 0.39 1.93 0.57
Im19 0.41 2.02 0.47
Im20 0.86 1.04 0.31
Im21 0.79 1.09 0.35
Im22 0.85 1.02 0.19
Number of factors = 6
Variable MR2 MR5 MR1 MR4 MR3 MR6 Complexity Uniqueness
Im1 1.05 1.06 0.16
Im2 1.03 1.07 0.24
Im3 0.99 1.03 0.15
Im4 1.06 1.05 0.08
Im5 0.74 1.03 0.45
Im6 0.52 0.68 2.22 0.29
Im7 0.65 0.56 2.24 0.22
Im8 0.80 1.05 0.26
Im9 0.48 1.95 0.54
Im10 0.81 1.23 0.22
Im11 0.67 1.15 0.55
Im12 0.91 1.03 0.27
Im13 0.79 1.09 0.30
Im14 0.80 1.18 0.24
Im15 0.60 1.18 0.37
Im16 0.46 1.81 0.53
Im17 0.57 1.97 0.30
Im18 0.54 1.91 0.43
Im19 0.39 2.15 0.48
Im20 0.92 1.07 0.21
Im21 0.76 1.07 0.35
Im22 0.80 1.04 0.21
Number of factors = 7
Variable MR5 MR1 MR2 MR3 MR4 MR7 MR6 Complexity Uniqueness
Im1 1.08 1.06 0.14
Im2 1.05 1.06 0.22
Im3 1.00 1.02 0.14
Im4 1.13 1.04 0.03
Im5 0.72 1.02 0.46
Im6 0.92 1.06 0.24
Im7 0.89 1.06 0.15
Im8 0.62 0.38 1.74 0.28
Im9 0.42 2.10 0.54
Im10 1.04 1.03 0.11
Im11 0.65 1.14 0.56
Im12 1.01 1.04 0.17
Im13 0.78 1.08 0.30
Im14 0.94 1.01 0.19
Im15 0.60 1.17 0.37
Im16 0.40 2.69 0.53
Im17 1.09 1.02 0.05
Im18 0.92 1.02 0.29
Im19 0.33 3.23 0.47
Im20 0.94 1.05 0.21
Im21 0.78 1.06 0.35
Im22 0.81 1.05 0.21
Number of factors = 8
Variable MR1 MR3 MR7 MR2 MR4 MR5 MR6 MR8 Complexity Uniqueness
Im1 1.04 1.01 0.06
Im2 0.95 1.02 0.19
Im3 0.90 1.02 0.14
Im4 1.03 1.03 0.03
Im5 0.72 1.11 0.42
Im6 0.98 1.06 0.24
Im7 0.95 1.05 0.15
Im8 0.43 0.49 2.39 0.28
Im9 0.45 1.92 0.54
Im10 0.97 1.01 0.10
Im11 0.66 1.15 0.55
Im12 1.04 1.05 0.16
Im13 0.79 1.06 0.30
Im14 0.92 1.02 0.15
Im15 0.35 0.36 2.73 0.35
Im16 1.02 1.03 0.20
Im17 0.98 1.01 0.07
Im18 0.90 1.01 0.26
Im19 0.63 1.11 0.38
Im20 0.98 1.09 0.19
Im21 0.79 1.06 0.35
Im22 0.82 1.06 0.22

7 factors: exclude 9, 15, 16, 19 6 factors: exclude 16, 17, 18, 19, 5 factors: exclude 17, 18

2.2 ROUND 2 : Exploratory factor analysis round 2

2.2.1 Variable selection for EFA

# # perform multiple variable selections
# 
# exclude <- list(c("Im1","Im2","Im16", "Im19","Im15","Im9"),
#              c("Im3","Im4","Im9", "Im15","Im11"))
# 
# survey_excl_img2 = list()
# data_img_EFA2 = list()
# 
# for (i in 1:length(exclude)){
#   survey_excl_img2[[i]] <- survey |> select(-exclude[[i]])
#   data_img_EFA2[[i]] <- survey_excl_img2[[i]][1:(22-length(exclude[[i]]))]
#   # print(survey_excl_img2[[i]])
# }
# 
# # survey_excl_img2[[1]]
# # survey_excl_img2[[2]]
# data_img_EFA2[[1]]
# data_img_EFA2[[2]]
# excluded image variables
# candidates for 7 factors: "Im9",("Im11"),"Im15", "Im19", "Im16"
# candidates for 6 factors: "Im16","Im9", "Im19", ("Im11"), ("Im15"), ("Im18"),"Im17", "Im6"

exclude=c("Im9","Im15","Im8") # "Im16", "Im19","Im9","Im11","Im15"

# the full survey data (includes dependent and independent variables) with excluded image variables
survey_excl_img2 <- survey |> select(-exclude) 

# the data we will use for EFA (images)
data_img_EFA2 <- survey_excl_img2[1:(22-length(exclude))]

The excluded variables correspond to the following:

excludedvars <- filter(labels, Variable %in% exclude)[c("Variable","Label_short")] 

excludedvars |>
  stable()
Variable Label_short
Im8 Expertise in French Traditional Cuisine
Im9 French Fashion
Im15 Professional Selection of Brands

2.2.2 handle missing data

# delete missing data
data_img_EFA2 <- na.omit(data_img_EFA2)

dim(survey)
## [1] 553  35
dim(survey_excl_img2)
## [1] 553  32
dim(data_img_EFA2)
## [1] 394  19

2.2.3 Check adequacy of correlation Matrix

2.2.3.1 correlation matrix

#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA2)
corrplot(as.matrix(corr_matrix), 
         method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
         order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
         addCoef.col = 'black', number.cex = .5,
         tl.col ="black", 
         tl.cex = 0.80,
         )

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

Variables to look out for going forward: - Images 9 and 11 are alone - Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).

2.2.3.2 Bartlett’s Test

bart_spher(data_img_EFA2)
##  Bartlett's Test of Sphericity
## 
## Call: bart_spher(x = data_img_EFA2)
## 
##      X2 = 5521.451
##      df = 171
## p-value < 2.22e-16

The Bartlett Test tests the hypothesis that the sample originates from a population, where all variables are uncorrelated. This would not be good for factor analysis, we want this hypothesis to be rejected meaning p-value < 5%.

In our case we see that it is indeed rejected and that the data is not uncorrelated.

2.2.3.3 KMO

KMOTEST=KMOS(data_img_EFA2)
print(KMOTEST, sort=T)
## 
## Kaiser-Meyer-Olkin Statistics
## 
## Call: KMOS(x = data_img_EFA2)
## 
## Measures of Sampling Adequacy (MSA):
##       Im6      Im10       Im7      Im14       Im2       Im1      Im20      Im18 
## 0.7471329 0.7642565 0.7744268 0.7843674 0.7950011 0.7961197 0.8143469 0.8323628 
##       Im4      Im17      Im12       Im3      Im13      Im22      Im11      Im16 
## 0.8394241 0.8427407 0.8483413 0.8497470 0.8567410 0.8730869 0.8958364 0.9007282 
##      Im21      Im19       Im5 
## 0.9102753 0.9199391 0.9515411 
## 
## KMO-Criterion: 0.8416876

The KMO of 0.8416876 is above 0.6 which indicates the data is well suited for factor anlysis.

2.2.3.4 Anti-image Correlation

MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))

#Display table
MSA_list<- MSA_list |> 
  setorder(cols = "MSA")
  
MSA_list |> 
  stable() |> 
  row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")
Item MSA
Im6 0.75
Im10 0.76
Im7 0.77
Im14 0.78
Im2 0.80
Im1 0.80
Im20 0.81
Im18 0.83
Im4 0.84
Im17 0.84
Im12 0.85
Im3 0.85
Im13 0.86
Im22 0.87
Im11 0.90
Im16 0.90
Im21 0.91
Im19 0.92
Im5 0.95

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

Variables with MSA values above 0.5 are suited for factor analysis. Presence of items with low MSA’s (<0.5) could also indicate that an important topic hasn’t been well covered in the questionnaire.

All variables have MSA above 0.5

2.2.4 Select method: PAF

2.2.4.1 Extract factors

EFA_PAF0 <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified
2.2.4.1.1 Scree plot
#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
     ylab="Eigenvalue",
     main="Scree plot",
     cex.lab=1.2,
     cex.axis=1.2,
     cex.main=1.8,
     col = "#0099F8",
     pch = 19) 
abline(h=1, col = "#7F35B2")

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

2.2.4.1.2 Kaiser Criterion
EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb
## [1] 6

The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.

There are 6 factors satisfying this condition.

2.2.4.1.3 Total Variance Explained
#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA2) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA2))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
                                            seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
                                          EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
                                          Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
                                          Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |> 
  stable()
Factor number EigenValue Variance Total_Variance
1 7.71 40.57 0.41
2 2.01 10.58 0.51
3 1.54 8.10 0.59
4 1.44 7.58 0.67
5 1.20 6.30 0.73
6 1.06 5.56 0.79
7 0.80 4.21 0.83
8 0.68 3.60 0.87
9 0.50 2.65 0.89
10 0.34 1.81 0.91
11 0.32 1.67 0.93
12 0.30 1.58 0.94
13 0.23 1.20 0.95
14 0.21 1.10 0.97
15 0.19 1.02 0.98
16 0.16 0.84 0.98
17 0.12 0.62 0.99
18 0.11 0.57 1.00
19 0.08 0.43 1.00

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

With 6 factors we would explain 78.6947762% of total variance.

With 7 factors we would explain 82.9058259% of total variance.

# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue
## [1] 7.109148

2.2.4.2 Determine number of factors to retain

# select nb of factors to test
nf = c(5,6,7,8)

2.2.4.3 PAF orthogonal Varimax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()

i=1
for (n in nf) {
  # EFA_PAFn[[i]] <- n
  EFA_PAFn[[i]] <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn) <- nf
2.2.4.3.1 Communalities
#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")

    EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn[[i]]$communality))

    # Sort table
    EFA_PAFn_communalities <- EFA_PAFn_communalities |>
      setorder(cols = "Communality")
    
    # Display table
    kbl <- EFA_PAFn_communalities |> 
              stable() |> 
              row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn[[i]]$loadings["Im6",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im6 =", communality))
    cat("\n")
    
}
Number of factors = 5
Item Communality
Im11 0.41
Im18 0.42
Im16 0.42
Im6 0.50
Im19 0.51
Im17 0.52
Im5 0.55
Im21 0.64
Im10 0.66
Im7 0.67
Im14 0.70
Im20 0.72
Im13 0.72
Im12 0.75
Im2 0.78
Im22 0.80
Im1 0.84
Im3 0.86
Im4 0.92

[1] “Communality for Im6 =0.496673139129337”

Number of factors = 6
Item Communality
Im16 0.42
Im11 0.45
Im19 0.51
Im5 0.55
Im6 0.64
Im21 0.64
Im18 0.65
Im13 0.69
Im10 0.71
Im7 0.73
Im12 0.74
Im14 0.74
Im20 0.78
Im22 0.79
Im2 0.80
Im17 0.83
Im3 0.86
Im1 0.89
Im4 0.92

[1] “Communality for Im6 =0.638799740882147”

Number of factors = 7
Item Communality
Im16 0.43
Im11 0.43
Im19 0.51
Im5 0.55
Im21 0.64
Im18 0.67
Im13 0.69
Im7 0.72
Im14 0.78
Im22 0.78
Im20 0.79
Im2 0.81
Im3 0.86
Im12 0.87
Im1 0.91
Im6 0.93
Im4 0.97
Im10 0.97
Im17 1.00

[1] “Communality for Im6 =0.931925021212407”

Number of factors = 8
Item Communality
Im11 0.43
Im5 0.58
Im21 0.64
Im16 0.67
Im18 0.68
Im13 0.69
Im7 0.69
Im19 0.70
Im2 0.76
Im14 0.78
Im22 0.78
Im20 0.81
Im3 0.86
Im12 0.87
Im4 0.97
Im6 0.99
Im10 1.00
Im17 1.00
Im1 1.00

[1] “Communality for Im6 =0.990898460352201”

Typically we should think about excluding variables with communalities below 0.3.

Based on the above, no variable should be excluded.

2.2.4.3.2 Factor loadings
# loadings for all selected number of factors

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
           
cat("\n\n")
}
Number of factors = 5
Variable MR1 MR2 MR4 MR5 MR3 Complexity Uniqueness
Im1 0.85 1.35 0.16
Im2 0.83 1.27 0.22
Im3 0.84 1.44 0.14
Im4 0.89 1.36 0.08
Im5 0.65 1.66 0.45
Im6 0.67 1.23 0.50
Im7 0.78 1.20 0.33
Im10 0.74 1.42 0.34
Im11 0.58 1.49 0.59
Im12 0.82 1.22 0.25
Im13 0.77 1.44 0.28
Im14 0.77 1.39 0.30
Im16 0.40 0.41 3.03 0.58
Im17 0.30 0.43 0.39 3.76 0.48
Im18 0.39 0.32 3.81 0.58
Im19 0.42 0.43 3.53 0.49
Im20 0.80 1.23 0.28
Im21 0.74 1.39 0.36
Im22 0.81 1.49 0.20
Number of factors = 6
Variable MR1 MR2 MR3 MR4 MR5 MR6 Complexity Uniqueness
Im1 0.86 1.40 0.11
Im2 0.83 1.33 0.20
Im3 0.85 1.43 0.14
Im4 0.89 1.35 0.08
Im5 0.65 1.63 0.45
Im6 0.73 1.40 0.36
Im7 0.81 1.24 0.27
Im10 0.70 0.32 1.95 0.29
Im11 0.61 1.46 0.55
Im12 0.80 1.31 0.26
Im13 0.71 1.80 0.31
Im14 0.73 0.32 1.85 0.26
Im16 0.41 0.39 3.16 0.58
Im17 0.74 2.15 0.17
Im18 0.66 2.10 0.35
Im19 0.43 0.39 3.93 0.49
Im20 0.84 1.21 0.22
Im21 0.73 1.43 0.36
Im22 0.79 1.54 0.21
Number of factors = 7
Variable MR1 MR3 MR4 MR5 MR2 MR6 MR7 Complexity Uniqueness
Im1 0.87 1.40 0.09
Im2 0.83 1.35 0.19
Im3 0.84 1.46 0.14
Im4 0.92 1.33 0.03
Im5 0.64 1.73 0.45
Im6 0.93 1.17 0.07
Im7 0.33 0.75 1.62 0.28
Im10 0.92 1.32 0.03
Im11 0.57 1.70 0.57
Im12 0.88 1.23 0.13
Im13 0.72 1.76 0.31
Im14 0.77 0.30 1.67 0.22
Im16 0.38 0.37 3.99 0.57
Im17 0.88 1.60 0.00
Im18 0.70 1.84 0.33
Im19 0.40 0.37 4.52 0.49
Im20 0.85 1.19 0.21
Im21 0.73 1.43 0.36
Im22 0.79 1.55 0.22
Number of factors = 8
Variable MR1 MR3 MR4 MR5 MR2 MR7 MR6 MR8 Complexity Uniqueness
Im1 0.91 1.44 0.00
Im2 0.78 1.56 0.24
Im3 0.82 1.63 0.14
Im4 0.89 1.46 0.03
Im5 0.66 1.78 0.42
Im6 0.96 1.15 0.01
Im7 0.34 0.72 1.69 0.31
Im10 0.93 1.32 0.00
Im11 0.57 1.71 0.57
Im12 0.89 1.22 0.13
Im13 0.72 1.76 0.31
Im14 0.77 1.68 0.22
Im16 0.68 2.03 0.33
Im17 0.88 1.65 0.00
Im18 0.70 1.84 0.32
Im19 0.64 2.71 0.30
Im20 0.86 1.19 0.19
Im21 0.73 1.44 0.36
Im22 0.79 1.56 0.22

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

Factor loadings:

  • Number of items per factor >=3
    • this condition is respected in all cases except when we have 8 factors. We eliminate the 8 factor solution
  • 0.40–0.30–0.20 rule: satisfactory variables (a) load onto their primary factor above 0.40, (b) load onto alter-native factors below 0.30, and (c) demonstrate a difference of 0.20 between their primary and alternative factor loadings.
    • 5 factor solution:
      • this condition is not respected for many variables. We eliminate the 5 factor solution
    • 6 factor solution:
      • this condition is not respected for: Im6, Im7, Im9, (Im11), (Im15), Im16, Im17, Im18, Im19 where Im17 and Im18 are particularly spread out
    • 7 factor solution:
      • this condition is not respected for: Im7, Im8, Im9, Im15, Im16, Im19 where Im16 and Im19 are particularly spread out

Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables, potentially 19 as it also has the lower communality than Im16 and probably also factor 9 as it also has low communality

Thurstone simple structure criteria:

  • Each row (variable) of the factor pattern matrix should have at least one zero

  • Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors

  • For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other

  • When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns

  • For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns

2.2.4.4 PAF oblique Promax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()

i=1
for (n in nf) {
  # EFA_PAFn_obl[[i]] <- n
  EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA2, rotate="promax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn_obl) <- nf

length(EFA_PAFn_obl)
## [1] 4
2.2.4.4.1 Communalities
#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")

    EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))

    # Sort table
    EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
      setorder(cols = "Communality")
    
    # Display table  
    kbl <- EFA_PAFn_obl_communalities |> 
              stable() |> 
              row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn_obl[[i]]$loadings["Im6",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im6 =", communality))
    cat("\n")
    
}
Number of factors = 5
Item Communality
Im11 0.41
Im18 0.42
Im16 0.42
Im6 0.50
Im19 0.51
Im17 0.52
Im5 0.55
Im21 0.64
Im10 0.66
Im7 0.67
Im14 0.70
Im20 0.72
Im13 0.72
Im12 0.75
Im2 0.78
Im22 0.80
Im1 0.84
Im3 0.86
Im4 0.92

[1] “Communality for Im6 =0.547199381232095”

Number of factors = 6
Item Communality
Im16 0.42
Im11 0.45
Im19 0.51
Im5 0.55
Im6 0.64
Im21 0.64
Im18 0.65
Im13 0.69
Im10 0.71
Im7 0.73
Im12 0.74
Im14 0.74
Im20 0.78
Im22 0.79
Im2 0.80
Im17 0.83
Im3 0.86
Im1 0.89
Im4 0.92

[1] “Communality for Im6 =0.833006250441541”

Number of factors = 7
Item Communality
Im16 0.43
Im11 0.43
Im19 0.51
Im5 0.55
Im21 0.64
Im18 0.67
Im13 0.69
Im7 0.72
Im14 0.78
Im22 0.78
Im20 0.79
Im2 0.81
Im3 0.86
Im12 0.87
Im1 0.91
Im6 0.93
Im4 0.97
Im10 0.97
Im17 1.00

[1] “Communality for Im6 =0.971113915290573”

Number of factors = 8
Item Communality
Im11 0.43
Im5 0.58
Im21 0.64
Im16 0.67
Im18 0.68
Im13 0.69
Im7 0.69
Im19 0.70
Im2 0.76
Im14 0.78
Im22 0.78
Im20 0.81
Im3 0.86
Im12 0.87
Im4 0.97
Im6 0.99
Im10 1.00
Im17 1.00
Im1 1.00

[1] “Communality for Im6 =1.14058133882705”

2.2.4.4.2 Factor loadings
# loadings for all selected number of factors

test = list()

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
      
cat("\n\n")
}
Number of factors = 5
Variable MR1 MR2 MR5 MR4 MR3 Complexity Uniqueness
Im1 1.06 1.05 0.16
Im2 1.06 1.07 0.22
Im3 1.05 1.04 0.14
Im4 1.11 1.05 0.08
Im5 0.77 1.03 0.45
Im6 0.72 1.12 0.50
Im7 0.85 1.15 0.33
Im10 0.75 1.21 0.34
Im11 0.68 1.09 0.59
Im12 1.00 1.04 0.25
Im13 0.89 1.02 0.28
Im14 0.78 1.14 0.30
Im16 0.33 0.36 2.14 0.58
Im17 0.34 2.56 0.48
Im18 0.31 2.71 0.58
Im19 0.32 0.36 2.28 0.49
Im20 0.88 1.07 0.28
Im21 0.78 1.06 0.36
Im22 0.84 1.02 0.20
Number of factors = 6
Variable MR1 MR2 MR3 MR5 MR4 MR6 Complexity Uniqueness
Im1 1.04 1.05 0.11
Im2 1.00 1.04 0.20
Im3 1.02 1.05 0.14
Im4 1.08 1.05 0.08
Im5 0.76 1.03 0.45
Im6 0.84 1.39 0.36
Im7 0.91 1.18 0.27
Im10 0.68 1.69 0.29
Im11 0.67 1.05 0.55
Im12 0.91 1.06 0.26
Im13 0.77 1.22 0.31
Im14 0.71 1.55 0.26
Im16 0.33 0.33 2.12 0.58
Im17 0.77 1.14 0.17
Im18 0.69 1.14 0.35
Im19 0.33 2.58 0.49
Im20 0.91 1.08 0.22
Im21 0.75 1.06 0.36
Im22 0.80 1.04 0.21
Number of factors = 7
Variable MR1 MR3 MR5 MR4 MR2 MR6 MR7 Complexity Uniqueness
Im1 1.07 1.05 0.09
Im2 1.02 1.03 0.19
Im3 1.01 1.02 0.14
Im4 1.14 1.05 0.03
Im5 0.73 1.02 0.45
Im6 0.98 1.04 0.07
Im7 0.73 1.16 0.28
Im10 1.10 1.03 0.03
Im11 0.60 1.16 0.57
Im12 1.00 1.03 0.13
Im13 0.75 1.11 0.31
Im14 0.87 1.04 0.22
Im16 3.60 0.57
Im17 1.12 1.02 0.00
Im18 0.86 1.03 0.33
Im19 3.47 0.49
Im20 0.94 1.04 0.21
Im21 0.77 1.05 0.36
Im22 0.82 1.03 0.22
Number of factors = 8
Variable MR1 MR3 MR4 MR2 MR5 MR6 MR7 MR8 Complexity Uniqueness
Im1 1.03 1.01 0.00
Im2 0.86 1.01 0.24
Im3 0.90 1.02 0.14
Im4 1.02 1.03 0.03
Im5 0.73 1.09 0.42
Im6 1.06 1.03 0.01
Im7 0.72 1.14 0.31
Im10 1.05 1.02 0.00
Im11 0.60 1.15 0.57
Im12 1.02 1.04 0.13
Im13 0.75 1.09 0.31
Im14 0.82 1.03 0.22
Im16 0.80 1.02 0.33
Im17 1.03 1.01 0.00
Im18 0.81 1.00 0.32
Im19 0.72 1.04 0.30
Im20 0.97 1.09 0.19
Im21 0.77 1.05 0.36
Im22 0.82 1.04 0.22

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

2.3 Confirmatory factor analysis

We test whether the constructs found in the exploratory phase adequately describe what is going on.

2.3.1 6 factor model

# no excluded variables
CFA_model_img_6f <- "
DECO =~ Im3 + Im4 + Im5
FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
QUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
BRAND =~ Im17 + Im18 + Im9
"

# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "

# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "

# CFA_fit_img <- cfa(CFA_model_img_6f, data=data_img_EFA, missing="ML")
CFA_fit_img_6f <- cfa(CFA_model_img_6f, data=survey, missing="ML")

summary(CFA_fit_img_6f, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6.15 ended normally after 110 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        81
## 
##   Number of observations                           553
##   Number of missing patterns                        87
## 
## Model Test User Model:
##                                                       
##   Test statistic                              1442.584
##   Degrees of freedom                               194
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                              8838.959
##   Degrees of freedom                               231
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.855
##   Tucker-Lewis Index (TLI)                       0.827
##                                                       
##   Robust Comparative Fit Index (CFI)             0.854
##   Robust Tucker-Lewis Index (TLI)                0.827
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -15479.697
##   Loglikelihood unrestricted model (H1)     -14758.405
##                                                       
##   Akaike (AIC)                               31121.394
##   Bayesian (BIC)                             31470.938
##   Sample-size adjusted Bayesian (SABIC)      31213.808
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.108
##   90 Percent confidence interval - lower         0.103
##   90 Percent confidence interval - upper         0.113
##   P-value H_0: RMSEA <= 0.050                    0.000
##   P-value H_0: RMSEA >= 0.080                    1.000
##                                                       
##   Robust RMSEA                                   0.110
##   90 Percent confidence interval - lower         0.105
##   90 Percent confidence interval - upper         0.116
##   P-value H_0: Robust RMSEA <= 0.050             0.000
##   P-value H_0: Robust RMSEA >= 0.080             1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.092
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.236    0.936
##     Im4               1.057    0.025   42.551    0.000    1.307    0.970
##     Im5               0.820    0.034   23.857    0.000    1.013    0.761
##   FRENCH =~                                                             
##     Im6               1.000                               0.642    0.535
##     Im7               1.219    0.106   11.525    0.000    0.783    0.644
##     Im8               1.244    0.099   12.567    0.000    0.799    0.755
##     Im10              1.251    0.095   13.133    0.000    0.803    0.914
##     Im14              1.244    0.095   13.142    0.000    0.799    0.929
##   ATMOS =~                                                              
##     Im20              1.000                               1.268    0.848
##     Im21              0.848    0.041   20.879    0.000    1.075    0.785
##     Im22              1.053    0.046   22.697    0.000    1.335    0.873
##   QUAL =~                                                               
##     Im11              1.000                               0.703    0.615
##     Im12              1.410    0.094   15.050    0.000    0.991    0.872
##     Im13              1.465    0.105   13.982    0.000    1.030    0.855
##   CHOICE =~                                                             
##     Im1               1.000                               1.232    0.926
##     Im2               0.942    0.027   34.780    0.000    1.160    0.902
##     Im15              0.720    0.036   20.097    0.000    0.887    0.740
##     Im16              0.567    0.041   13.849    0.000    0.699    0.579
##     Im19              0.540    0.038   14.310    0.000    0.666    0.592
##   BRAND =~                                                              
##     Im17              1.000                               1.184    0.952
##     Im18              1.025    0.038   27.280    0.000    1.214    0.868
##     Im9               0.540    0.047   11.386    0.000    0.640    0.474
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FRENCH            0.344    0.046    7.416    0.000    0.434    0.434
##     ATMOS             0.730    0.082    8.901    0.000    0.466    0.466
##     QUAL              0.409    0.051    8.040    0.000    0.471    0.471
##     CHOICE            0.782    0.079    9.940    0.000    0.514    0.514
##     BRAND             0.778    0.076   10.268    0.000    0.531    0.531
##   FRENCH ~~                                                             
##     ATMOS             0.265    0.045    5.888    0.000    0.326    0.326
##     QUAL              0.206    0.030    6.812    0.000    0.456    0.456
##     CHOICE            0.299    0.044    6.737    0.000    0.378    0.378
##     BRAND             0.277    0.042    6.547    0.000    0.364    0.364
##   ATMOS ~~                                                              
##     QUAL              0.373    0.053    7.021    0.000    0.419    0.419
##     CHOICE            0.767    0.083    9.216    0.000    0.491    0.491
##     BRAND             0.792    0.081    9.797    0.000    0.528    0.528
##   QUAL ~~                                                               
##     CHOICE            0.460    0.054    8.585    0.000    0.531    0.531
##     BRAND             0.483    0.053    9.113    0.000    0.581    0.581
##   CHOICE ~~                                                             
##     BRAND             0.864    0.078   11.040    0.000    0.592    0.592
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.994    0.056   88.528    0.000    4.994    3.785
##    .Im4               4.997    0.057   86.919    0.000    4.997    3.709
##    .Im5               5.034    0.057   87.796    0.000    5.034    3.785
##    .Im6               5.824    0.051  113.338    0.000    5.824    4.849
##    .Im7               5.751    0.053  109.497    0.000    5.751    4.727
##    .Im8               6.000    0.045  133.008    0.000    6.000    5.671
##    .Im10              6.100    0.037  163.041    0.000    6.100    6.945
##    .Im14              6.139    0.037  166.909    0.000    6.139    7.138
##    .Im20              4.672    0.064   73.182    0.000    4.672    3.124
##    .Im21              5.139    0.058   87.973    0.000    5.139    3.751
##    .Im22              4.278    0.065   65.391    0.000    4.278    2.798
##    .Im11              5.653    0.049  115.277    0.000    5.653    4.943
##    .Im12              5.666    0.049  116.095    0.000    5.666    4.983
##    .Im13              5.448    0.052  105.630    0.000    5.448    4.525
##    .Im1               4.792    0.057   84.316    0.000    4.792    3.601
##    .Im2               4.861    0.055   88.357    0.000    4.861    3.779
##    .Im15              5.090    0.051   99.219    0.000    5.090    4.246
##    .Im16              5.130    0.052   98.387    0.000    5.130    4.251
##    .Im19              5.146    0.048  106.829    0.000    5.146    4.578
##    .Im17              5.025    0.053   94.490    0.000    5.025    4.038
##    .Im18              4.595    0.060   76.460    0.000    4.595    3.286
##    .Im9               5.075    0.058   87.318    0.000    5.075    3.757
##     DECO              0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     QUAL              0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.215    0.024    8.776    0.000    0.215    0.123
##    .Im4               0.108    0.024    4.439    0.000    0.108    0.060
##    .Im5               0.744    0.049   15.192    0.000    0.744    0.421
##    .Im6               1.030    0.066   15.665    0.000    1.030    0.714
##    .Im7               0.867    0.059   14.739    0.000    0.867    0.586
##    .Im8               0.482    0.034   14.159    0.000    0.482    0.430
##    .Im10              0.127    0.013    9.840    0.000    0.127    0.164
##    .Im14              0.101    0.012    8.329    0.000    0.101    0.137
##    .Im20              0.629    0.061   10.379    0.000    0.629    0.281
##    .Im21              0.721    0.057   12.668    0.000    0.721    0.384
##    .Im22              0.554    0.063    8.781    0.000    0.554    0.237
##    .Im11              0.814    0.055   14.805    0.000    0.814    0.622
##    .Im12              0.310    0.039    7.857    0.000    0.310    0.240
##    .Im13              0.390    0.044    8.777    0.000    0.390    0.269
##    .Im1               0.253    0.035    7.312    0.000    0.253    0.143
##    .Im2               0.308    0.033    9.422    0.000    0.308    0.186
##    .Im15              0.651    0.048   13.673    0.000    0.651    0.453
##    .Im16              0.968    0.065   14.927    0.000    0.968    0.664
##    .Im19              0.820    0.055   14.954    0.000    0.820    0.649
##    .Im17              0.146    0.036    4.039    0.000    0.146    0.094
##    .Im18              0.482    0.046   10.494    0.000    0.482    0.247
##    .Im9               1.415    0.089   15.908    0.000    1.415    0.776
##     DECO              1.527    0.107   14.308    0.000    1.000    1.000
##     FRENCH            0.412    0.064    6.422    0.000    1.000    1.000
##     ATMOS             1.608    0.138   11.683    0.000    1.000    1.000
##     QUAL              0.494    0.067    7.365    0.000    1.000    1.000
##     CHOICE            1.518    0.110   13.746    0.000    1.000    1.000
##     BRAND             1.402    0.100   14.036    0.000    1.000    1.000

2.3.1.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.3.1.2 local fit measures

# semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5, 
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
         rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
         nCharNodes = 7,shapeMan = "rectangle", 
         sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
         curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
         )

lambda = inspect(CFA_fit_img_6f, what="std")$lambda
theta = inspect(CFA_fit_img_6f, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones
2.3.1.2.1 Indicator reliability criterion
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail
##      DECO FRENCH ATMOS  QUAL CHOICE BRAND
## Im3   NaN    NaN   NaN   NaN    NaN   NaN
## Im4   NaN    NaN   NaN   NaN    NaN   NaN
## Im5   NaN    NaN   NaN   NaN    NaN   NaN
## Im6   NaN  0.286   NaN   NaN    NaN   NaN
## Im7   NaN    NaN   NaN   NaN    NaN   NaN
## Im8   NaN    NaN   NaN   NaN    NaN   NaN
## Im10  NaN    NaN   NaN   NaN    NaN   NaN
## Im14  NaN    NaN   NaN   NaN    NaN   NaN
## Im20  NaN    NaN   NaN   NaN    NaN   NaN
## Im21  NaN    NaN   NaN   NaN    NaN   NaN
## Im22  NaN    NaN   NaN   NaN    NaN   NaN
## Im11  NaN    NaN   NaN 0.378    NaN   NaN
## Im12  NaN    NaN   NaN   NaN    NaN   NaN
## Im13  NaN    NaN   NaN   NaN    NaN   NaN
## Im1   NaN    NaN   NaN   NaN    NaN   NaN
## Im2   NaN    NaN   NaN   NaN    NaN   NaN
## Im15  NaN    NaN   NaN   NaN    NaN   NaN
## Im16  NaN    NaN   NaN   NaN  0.336   NaN
## Im19  NaN    NaN   NaN   NaN  0.351   NaN
## Im17  NaN    NaN   NaN   NaN    NaN   NaN
## Im18  NaN    NaN   NaN   NaN    NaN   NaN
## Im9   NaN    NaN   NaN   NaN    NaN 0.224
2.3.1.2.2 Construct reliability criterion
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail
##        DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO    NaN    NaN   NaN  NaN    NaN   NaN
## FRENCH  NaN    NaN   NaN  NaN    NaN   NaN
## ATMOS   NaN    NaN   NaN  NaN    NaN   NaN
## QUAL    NaN    NaN   NaN  NaN    NaN   NaN
## CHOICE  NaN    NaN   NaN  NaN    NaN   NaN
## BRAND   NaN    NaN   NaN  NaN    NaN   NaN
2.3.1.2.3 Average Variance Extracted criterion
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail
##        DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO    NaN    NaN   NaN  NaN    NaN   NaN
## FRENCH  NaN    NaN   NaN  NaN    NaN   NaN
## ATMOS   NaN    NaN   NaN  NaN    NaN   NaN
## QUAL    NaN    NaN   NaN  NaN    NaN   NaN
## CHOICE  NaN    NaN   NaN  NaN    NaN   NaN
## BRAND   NaN    NaN   NaN  NaN    NaN   NaN
2.3.1.2.4 Fornell-Larcker Criteria
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_6f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail
##        DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO      1                               
## FRENCH  NaN      1                        
## ATMOS   NaN    NaN     1                  
## QUAL    NaN    NaN   NaN    1             
## CHOICE  NaN    NaN   NaN  NaN      1      
## BRAND   NaN    NaN   NaN  NaN    NaN     1
# AVE should be higher than squared correlations between constructs

# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices any psi bigger than AVE will be negative
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full
##             DECO    FRENCH     ATMOS      QUAL    CHOICE     BRAND
## DECO   0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## FRENCH 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## ATMOS  0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## QUAL   0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## CHOICE 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## BRAND  0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
psi
##         DECO FRENCH ATMOS  QUAL CHOICE BRAND
## DECO   1.000                                
## FRENCH 0.434  1.000                         
## ATMOS  0.466  0.326 1.000                   
## QUAL   0.471  0.456 0.419 1.000             
## CHOICE 0.514  0.378 0.491 0.531  1.000      
## BRAND  0.531  0.364 0.528 0.581  0.592 1.000
AVEpsi_fail
##          DECO FRENCH  ATMOS   QUAL CHOICE  BRAND
## DECO        .                                   
## FRENCH    NaN      .                            
## ATMOS     NaN    NaN      .                     
## QUAL      NaN    NaN    NaN      .              
## CHOICE    NaN    NaN    NaN    NaN      .       
## BRAND     NaN    NaN    NaN    NaN -0.011      .

2.3.1.3 Modification indices

arrange(modificationindices(CFA_fit_img_6f),-mi)
##        lhs op  rhs      mi    epc sepc.lv sepc.all sepc.nox
## 1      Im1 ~~  Im2 495.934  0.951   0.951    3.408    3.408
## 2     Im10 ~~ Im14 298.631  0.357   0.357    3.154    3.154
## 3      Im6 ~~  Im7 255.917  0.693   0.693    0.734    0.734
## 4     Im16 ~~ Im19 128.231  0.463   0.463    0.519    0.519
## 5      Im7 ~~  Im8 104.366  0.316   0.316    0.489    0.489
## 6     DECO =~ Im19  76.462  0.344   0.424    0.378    0.378
## 7   FRENCH =~  Im9  73.482  0.783   0.503    0.372    0.372
## 8      Im6 ~~ Im10  55.895 -0.158  -0.158   -0.438   -0.438
## 9      Im1 ~~ Im16  55.410 -0.242  -0.242   -0.489   -0.489
## 10    QUAL =~ Im15  54.596  0.510   0.359    0.299    0.299
## 11     Im6 ~~  Im8  52.130  0.236   0.236    0.335    0.335
## 12     Im7 ~~ Im14  50.063 -0.145  -0.145   -0.491   -0.491
## 13  FRENCH =~ Im19  49.872  0.497   0.319    0.284    0.284
## 14    Im15 ~~ Im16  49.062  0.263   0.263    0.332    0.332
## 15     Im1 ~~ Im19  46.763 -0.204  -0.204   -0.449   -0.449
## 16    QUAL =~  Im9  45.834  0.702   0.494    0.365    0.365
## 17     Im2 ~~ Im19  45.384 -0.198  -0.198   -0.393   -0.393
## 18     Im7 ~~  Im9  45.214  0.340   0.340    0.307    0.307
## 19    DECO =~ Im16  44.633  0.288   0.356    0.295    0.295
## 20   BRAND =~ Im19  43.739  0.300   0.355    0.316    0.316
## 21     Im7 ~~ Im10  41.088 -0.134  -0.134   -0.406   -0.406
## 22    QUAL =~  Im2  38.006 -0.361  -0.254   -0.197   -0.197
## 23   BRAND =~ Im15  37.135  0.254   0.301    0.251    0.251
## 24    Im17 ~~ Im18  36.588  0.762   0.762    2.870    2.870
## 25     Im2 ~~ Im15  35.103 -0.179  -0.179   -0.399   -0.399
## 26    Im15 ~~ Im19  34.736  0.202   0.202    0.277    0.277
## 27    QUAL =~ Im19  33.294  0.434   0.305    0.271    0.271
## 28     Im8 ~~ Im14  32.038 -0.103  -0.103   -0.467   -0.467
## 29     Im6 ~~  Im9  31.342  0.301   0.301    0.249    0.249
## 30     Im1 ~~ Im15  30.586 -0.174  -0.174   -0.429   -0.429
## 31     Im2 ~~ Im16  28.333 -0.170  -0.170   -0.311   -0.311
## 32    DECO =~ Im15  27.803  0.191   0.236    0.197    0.197
## 33     Im6 ~~ Im14  27.360 -0.108  -0.108   -0.335   -0.335
## 34  FRENCH =~ Im16  27.263  0.403   0.259    0.214    0.214
## 35    DECO =~  Im2  26.666 -0.158  -0.195   -0.152   -0.152
## 36   ATMOS =~ Im15  24.669  0.181   0.230    0.192    0.192
## 37   BRAND =~ Im13  23.589  0.232   0.275    0.228    0.228
## 38    DECO =~  Im1  22.892 -0.149  -0.184   -0.138   -0.138
## 39   ATMOS =~  Im2  21.308 -0.142  -0.180   -0.140   -0.140
## 40    Im11 ~~ Im13  21.300 -0.191  -0.191   -0.339   -0.339
## 41   BRAND =~  Im2  21.047 -0.165  -0.195   -0.152   -0.152
## 42  FRENCH =~  Im1  20.125 -0.244  -0.156   -0.118   -0.118
## 43  FRENCH =~ Im15  18.582  0.279   0.179    0.149    0.149
## 44   BRAND =~ Im12  18.526 -0.197  -0.233   -0.205   -0.205
## 45   BRAND =~ Im16  17.630  0.209   0.247    0.205    0.205
## 46   BRAND =~  Im1  16.671 -0.150  -0.177   -0.133   -0.133
## 47   ATMOS =~ Im19  16.384  0.161   0.204    0.181    0.181
## 48   BRAND =~  Im6  14.589  0.161   0.191    0.159    0.159
## 49  CHOICE =~ Im20  14.430 -0.169  -0.208   -0.139   -0.139
## 50    Im14 ~~  Im9  13.864 -0.082  -0.082   -0.217   -0.217
## 51    Im11 ~~ Im12  13.374  0.145   0.145    0.289    0.289
## 52    Im21 ~~ Im22  13.217 -0.270  -0.270   -0.427   -0.427
## 53  CHOICE =~ Im13  13.044  0.152   0.187    0.155    0.155
## 54   ATMOS =~  Im7  12.806  0.134   0.170    0.140    0.140
## 55     Im8 ~~ Im10  12.666 -0.065  -0.065   -0.265   -0.265
## 56  FRENCH =~ Im11  12.345  0.269   0.173    0.151    0.151
## 57  CHOICE =~ Im12  11.541 -0.136  -0.168   -0.148   -0.148
## 58     Im3 ~~  Im4  11.447  0.264   0.264    1.735    1.735
## 59   ATMOS =~ Im16  11.243  0.146   0.185    0.153    0.153
## 60   ATMOS =~ Im12  11.072 -0.115  -0.146   -0.128   -0.128
## 61     Im8 ~~  Im9  10.943  0.125   0.125    0.152    0.152
## 62  FRENCH =~  Im2  10.891 -0.177  -0.114   -0.088   -0.088
## 63     Im7 ~~ Im22  10.253  0.126   0.126    0.182    0.182
## 64    DECO =~  Im9  10.194  0.167   0.207    0.153    0.153
## 65    Im11 ~~  Im9  10.067  0.156   0.156    0.145    0.145
## 66    Im15 ~~  Im9   9.926  0.139   0.139    0.145    0.145
## 67    QUAL =~ Im16   9.231  0.250   0.176    0.146    0.146
## 68     Im8 ~~ Im15   9.159  0.080   0.080    0.144    0.144
## 69   ATMOS =~  Im9   9.070  0.162   0.205    0.152    0.152
## 70    Im13 ~~ Im17   9.051  0.067   0.067    0.281    0.281
## 71     Im6 ~~ Im22   8.985  0.125   0.125    0.166    0.166
## 72    Im20 ~~ Im21   8.930  0.206   0.206    0.306    0.306
## 73   BRAND =~ Im22   8.880  0.147   0.175    0.114    0.114
## 74     Im8 ~~ Im16   8.801  0.095   0.095    0.139    0.139
## 75   BRAND =~ Im20   8.486 -0.141  -0.167   -0.111   -0.111
## 76   BRAND =~  Im7   8.244  0.114   0.135    0.111    0.111
## 77     Im3 ~~  Im1   8.143 -0.045  -0.045   -0.194   -0.194
## 78     Im8 ~~  Im2   7.823 -0.059  -0.059   -0.153   -0.153
## 79    QUAL =~ Im18   7.388 -0.230  -0.161   -0.115   -0.115
## 80    Im10 ~~ Im16   7.338  0.052   0.052    0.149    0.149
## 81    Im13 ~~  Im1   7.263  0.060   0.060    0.191    0.191
## 82     Im4 ~~ Im17   7.109 -0.041  -0.041   -0.322   -0.322
## 83    Im22 ~~ Im12   7.028 -0.078  -0.078   -0.189   -0.189
## 84    Im17 ~~  Im9   7.005 -0.112  -0.112   -0.247   -0.247
## 85    DECO =~  Im6   6.969  0.109   0.134    0.112    0.112
## 86   ATMOS =~ Im11   6.857  0.102   0.130    0.113    0.113
## 87  CHOICE =~  Im9   6.692  0.148   0.182    0.135    0.135
## 88   ATMOS =~  Im6   6.616  0.102   0.130    0.108    0.108
## 89    Im14 ~~  Im2   6.285  0.031   0.031    0.175    0.175
## 90   BRAND =~  Im5   6.246  0.103   0.122    0.092    0.092
## 91   BRAND =~  Im4   6.180 -0.071  -0.084   -0.062   -0.062
## 92    Im22 ~~  Im9   5.999  0.121   0.121    0.136    0.136
## 93    QUAL =~  Im5   5.978  0.169   0.119    0.089    0.089
## 94     Im1 ~~  Im9   5.822 -0.084  -0.084   -0.140   -0.140
## 95    QUAL =~  Im1   5.747 -0.143  -0.100   -0.075   -0.075
## 96  CHOICE =~ Im18   5.737 -0.115  -0.141   -0.101   -0.101
## 97     Im3 ~~  Im5   5.693 -0.084  -0.084   -0.209   -0.209
## 98     Im8 ~~ Im22   5.661  0.070   0.070    0.136    0.136
## 99    DECO =~ Im20   5.578 -0.100  -0.123   -0.082   -0.082
## 100  ATMOS =~  Im5   5.473  0.089   0.112    0.084    0.084
## 101   DECO =~ Im17   5.404 -0.091  -0.112   -0.090   -0.090
## 102   Im11 ~~ Im17   5.351 -0.061  -0.061   -0.177   -0.177
## 103 CHOICE =~  Im5   5.052  0.088   0.108    0.082    0.082
## 104 FRENCH =~ Im13   4.802 -0.157  -0.101   -0.084   -0.084
## 105   DECO =~ Im22   4.756  0.094   0.116    0.076    0.076
## 106   Im22 ~~ Im11   4.722  0.083   0.083    0.124    0.124
## 107 CHOICE =~ Im22   4.719  0.099   0.122    0.080    0.080
## 108   Im13 ~~ Im16   4.625 -0.073  -0.073   -0.118   -0.118
## 109   Im19 ~~ Im17   4.621  0.056   0.056    0.161    0.161
## 110  ATMOS =~ Im10   4.609 -0.038  -0.048   -0.055   -0.055
## 111  BRAND =~ Im10   4.570 -0.040  -0.048   -0.054   -0.054
## 112   Im14 ~~ Im22   4.494 -0.036  -0.036   -0.154   -0.154
## 113  ATMOS =~  Im4   4.422 -0.053  -0.067   -0.050   -0.050
## 114   Im14 ~~ Im15   4.415 -0.032  -0.032   -0.127   -0.127
## 115   Im21 ~~  Im9   4.370 -0.102  -0.102   -0.101   -0.101
## 116   Im10 ~~ Im13   4.362 -0.031  -0.031   -0.138   -0.138
## 117    Im7 ~~ Im15   4.358  0.074   0.074    0.098    0.098
## 118    Im3 ~~ Im22   4.300  0.047   0.047    0.135    0.135
## 119   Im20 ~~  Im1   4.283 -0.056  -0.056   -0.141   -0.141
## 120    Im4 ~~ Im16   4.262  0.048   0.048    0.149    0.149
## 121 FRENCH =~  Im5   4.167  0.144   0.093    0.070    0.070
## 122  ATMOS =~  Im8   4.061  0.057   0.072    0.068    0.068
## 123    Im6 ~~ Im20   4.039 -0.084  -0.084   -0.105   -0.105
## 124   Im10 ~~ Im11   4.002  0.036   0.036    0.111    0.111
## 125   Im20 ~~ Im17   3.990 -0.054  -0.054   -0.177   -0.177
## 126    Im6 ~~ Im11   3.977 -0.083  -0.083   -0.091   -0.091
## 127    Im5 ~~  Im1   3.869  0.051   0.051    0.117    0.117
## 128   Im15 ~~ Im17   3.695  0.045   0.045    0.147    0.147
## 129    Im4 ~~ Im18   3.604  0.035   0.035    0.152    0.152
## 130   Im12 ~~ Im15   3.556  0.050   0.050    0.110    0.110
## 131 FRENCH =~ Im17   3.536 -0.115  -0.074   -0.060   -0.060
## 132   Im14 ~~ Im16   3.474 -0.035  -0.035   -0.110   -0.110
## 133    Im3 ~~ Im15   3.381  0.037   0.037    0.099    0.099
## 134    Im3 ~~ Im17   3.375  0.029   0.029    0.161    0.161
## 135    Im3 ~~ Im19   3.371  0.040   0.040    0.096    0.096
## 136   Im13 ~~ Im15   3.338  0.051   0.051    0.102    0.102
## 137   Im22 ~~  Im1   3.275  0.049   0.049    0.132    0.132
## 138   Im20 ~~ Im13   3.270  0.057   0.057    0.115    0.115
## 139   Im13 ~~  Im2   3.219 -0.040  -0.040   -0.116   -0.116
## 140   Im11 ~~  Im1   3.071 -0.047  -0.047   -0.104   -0.104
## 141 CHOICE =~ Im21   3.048  0.074   0.091    0.066    0.066
## 142   Im10 ~~ Im17   3.000 -0.021  -0.021   -0.157   -0.157
## 143  ATMOS =~  Im1   2.962 -0.054  -0.068   -0.051   -0.051
## 144  ATMOS =~ Im13   2.889  0.062   0.078    0.065    0.065
## 145   Im16 ~~  Im9   2.810  0.089   0.089    0.076    0.076
## 146    Im5 ~~ Im14   2.794  0.028   0.028    0.101    0.101
## 147    Im4 ~~ Im22   2.701 -0.036  -0.036   -0.146   -0.146
## 148 CHOICE =~ Im10   2.670 -0.030  -0.037   -0.042   -0.042
## 149    Im1 ~~ Im17   2.662 -0.031  -0.031   -0.161   -0.161
## 150  ATMOS =~ Im14   2.649 -0.028  -0.035   -0.041   -0.041
## 151    Im4 ~~ Im19   2.526  0.034   0.034    0.113    0.113
## 152    Im4 ~~ Im11   2.492 -0.034  -0.034   -0.115   -0.115
## 153   Im21 ~~ Im18   2.456 -0.050  -0.050   -0.086   -0.086
## 154   Im12 ~~  Im2   2.343 -0.032  -0.032   -0.104   -0.104
## 155    Im6 ~~ Im15   2.316  0.057   0.057    0.070    0.070
## 156   Im12 ~~  Im9   2.302  0.057   0.057    0.086    0.086
## 157   DECO =~ Im12   2.287 -0.054  -0.067   -0.059   -0.059
## 158    Im6 ~~  Im1   2.248 -0.044  -0.044   -0.087   -0.087
## 159    Im3 ~~ Im20   2.237 -0.034  -0.034   -0.091   -0.091
## 160   Im15 ~~ Im18   2.236 -0.043  -0.043   -0.077   -0.077
## 161    Im7 ~~  Im1   2.236 -0.042  -0.042   -0.089   -0.089
## 162    Im6 ~~ Im12   2.164 -0.047  -0.047   -0.083   -0.083
## 163   Im10 ~~ Im12   2.160  0.020   0.020    0.102    0.102
## 164    Im4 ~~  Im2   2.090 -0.022  -0.022   -0.123   -0.123
## 165    Im5 ~~  Im6   1.873 -0.055  -0.055   -0.063   -0.063
## 166    Im4 ~~  Im6   1.846  0.032   0.032    0.096    0.096
## 167   DECO =~ Im10   1.832 -0.025  -0.031   -0.035   -0.035
## 168   Im22 ~~  Im2   1.825 -0.037  -0.037   -0.090   -0.090
## 169   Im10 ~~ Im22   1.781 -0.024  -0.024   -0.090   -0.090
## 170   Im12 ~~ Im17   1.776 -0.028  -0.028   -0.131   -0.131
## 171    Im6 ~~ Im18   1.754  0.047   0.047    0.066    0.066
## 172   Im21 ~~ Im17   1.749  0.035   0.035    0.108    0.108
## 173    Im5 ~~ Im16   1.746 -0.052  -0.052   -0.062   -0.062
## 174    Im3 ~~ Im12   1.732 -0.023  -0.023   -0.087   -0.087
## 175   Im22 ~~ Im13   1.726 -0.041  -0.041   -0.089   -0.089
## 176   Im18 ~~  Im9   1.696 -0.060  -0.060   -0.073   -0.073
## 177  ATMOS =~ Im17   1.682 -0.052  -0.065   -0.053   -0.053
## 178   QUAL =~  Im4   1.672 -0.060  -0.042   -0.031   -0.031
## 179   Im20 ~~ Im19   1.649  0.048   0.048    0.067    0.067
## 180   Im20 ~~  Im2   1.631 -0.035  -0.035   -0.080   -0.080
## 181 FRENCH =~ Im18   1.599 -0.082  -0.052   -0.038   -0.038
## 182    Im4 ~~ Im12   1.546  0.021   0.021    0.113    0.113
## 183 CHOICE =~ Im17   1.544  0.057   0.071    0.057    0.057
## 184    Im6 ~~ Im19   1.483  0.050   0.050    0.055    0.055
## 185   Im12 ~~ Im16   1.481  0.038   0.038    0.070    0.070
## 186    Im7 ~~ Im16   1.479 -0.052  -0.052   -0.056   -0.056
## 187   DECO =~ Im13   1.462  0.045   0.056    0.046    0.046
## 188 FRENCH =~ Im20   1.442 -0.089  -0.057   -0.038   -0.038
## 189   Im12 ~~ Im13   1.442  0.089   0.089    0.255    0.255
## 190  BRAND =~  Im3   1.434  0.033   0.039    0.030    0.030
## 191   Im12 ~~  Im1   1.360 -0.024  -0.024   -0.087   -0.087
## 192    Im3 ~~ Im18   1.301 -0.022  -0.022   -0.067   -0.067
## 193   Im16 ~~ Im17   1.269  0.032   0.032    0.085    0.085
## 194    Im3 ~~ Im11   1.261  0.025   0.025    0.060    0.060
## 195   Im14 ~~ Im17   1.252  0.013   0.013    0.110    0.110
## 196   Im10 ~~ Im19   1.233  0.019   0.019    0.060    0.060
## 197    Im3 ~~ Im10   1.230  0.012   0.012    0.070    0.070
## 198    Im8 ~~ Im18   1.200 -0.027  -0.027   -0.057   -0.057
## 199    Im8 ~~  Im1   1.194 -0.023  -0.023   -0.065   -0.065
## 200   Im21 ~~  Im2   1.185  0.030   0.030    0.063    0.063
## 201   QUAL =~ Im22   1.168 -0.084  -0.059   -0.038   -0.038
## 202 CHOICE =~ Im14   1.154  0.019   0.023    0.027    0.027
## 203   Im10 ~~  Im9   1.119  0.024   0.024    0.057    0.057
## 204   DECO =~ Im18   1.115  0.043   0.053    0.038    0.038
## 205 CHOICE =~  Im4   1.111 -0.028  -0.035   -0.026   -0.026
## 206   Im14 ~~ Im21   1.104  0.018   0.018    0.067    0.067
## 207    Im5 ~~ Im19   1.093 -0.038  -0.038   -0.048   -0.048
## 208    Im4 ~~  Im8   1.089  0.017   0.017    0.076    0.076
## 209   Im22 ~~ Im18   1.078  0.034   0.034    0.065    0.065
## 210   Im22 ~~ Im15   1.067  0.036   0.036    0.059    0.059
## 211   Im13 ~~ Im18   1.031 -0.027  -0.027   -0.062   -0.062
## 212 CHOICE =~  Im7   0.941  0.037   0.046    0.038    0.038
## 213    Im4 ~~ Im10   0.906 -0.010  -0.010   -0.082   -0.082
## 214    Im3 ~~ Im14   0.890 -0.010  -0.010   -0.065   -0.065
## 215   Im10 ~~  Im2   0.889 -0.012  -0.012   -0.061   -0.061
## 216  ATMOS =~  Im3   0.869  0.023   0.029    0.022    0.022
## 217   Im11 ~~ Im16   0.846  0.038   0.038    0.043    0.043
## 218   QUAL =~ Im14   0.840  0.031   0.022    0.026    0.026
## 219   QUAL =~ Im20   0.837  0.069   0.049    0.033    0.033
## 220    Im1 ~~ Im18   0.830  0.021   0.021    0.060    0.060
## 221    Im3 ~~ Im16   0.818  0.022   0.022    0.048    0.048
## 222   DECO =~  Im7   0.814  0.035   0.043    0.036    0.036
## 223    Im2 ~~ Im18   0.811 -0.021  -0.021   -0.054   -0.054
## 224   Im20 ~~ Im12   0.794  0.026   0.026    0.059    0.059
## 225 FRENCH =~ Im22   0.781  0.067   0.043    0.028    0.028
## 226   Im20 ~~ Im16   0.767  0.036   0.036    0.046    0.046
## 227   Im14 ~~ Im18   0.739 -0.012  -0.012   -0.056   -0.056
## 228   Im22 ~~ Im19   0.717 -0.032  -0.032   -0.047   -0.047
## 229   QUAL =~ Im10   0.654 -0.028  -0.020   -0.023   -0.023
## 230   Im14 ~~ Im13   0.649  0.011   0.011    0.057    0.057
## 231   Im14 ~~ Im11   0.639  0.014   0.014    0.048    0.048
## 232 CHOICE =~  Im6   0.612  0.032   0.039    0.033    0.033
## 233   Im19 ~~  Im9   0.595  0.037   0.037    0.035    0.035
## 234  BRAND =~ Im11   0.591 -0.036  -0.043   -0.038   -0.038
## 235    Im6 ~~  Im2   0.577 -0.023  -0.023   -0.040   -0.040
## 236   Im20 ~~ Im15   0.576  0.026   0.026    0.041    0.041
## 237    Im5 ~~ Im22   0.561  0.027   0.027    0.043    0.043
## 238    Im8 ~~ Im19   0.558  0.022   0.022    0.035    0.035
## 239    Im8 ~~ Im21   0.538 -0.022  -0.022   -0.037   -0.037
## 240   Im21 ~~ Im12   0.537  0.021   0.021    0.045    0.045
## 241   Im11 ~~ Im19   0.536  0.028   0.028    0.034    0.034
## 242   Im21 ~~  Im1   0.534  0.020   0.020    0.046    0.046
## 243   QUAL =~  Im7   0.517  0.053   0.037    0.031    0.031
## 244   Im10 ~~ Im18   0.516  0.011   0.011    0.044    0.044
## 245    Im5 ~~ Im11   0.511  0.026   0.026    0.034    0.034
## 246   Im10 ~~ Im20   0.483  0.012   0.012    0.044    0.044
## 247   Im12 ~~ Im18   0.465 -0.017  -0.017   -0.044   -0.044
## 248   Im14 ~~  Im1   0.460  0.008   0.008    0.052    0.052
## 249 FRENCH =~  Im3   0.457 -0.031  -0.020   -0.015   -0.015
## 250   Im20 ~~ Im11   0.453  0.026   0.026    0.036    0.036
## 251    Im3 ~~  Im8   0.442 -0.012  -0.012   -0.036   -0.036
## 252   Im20 ~~ Im18   0.417  0.021   0.021    0.038    0.038
## 253   Im20 ~~ Im22   0.407  0.061   0.061    0.103    0.103
## 254   Im10 ~~  Im1   0.405 -0.008  -0.008   -0.045   -0.045
## 255    Im5 ~~ Im20   0.402  0.023   0.023    0.034    0.034
## 256  BRAND =~ Im14   0.390 -0.011  -0.014   -0.016   -0.016
## 257    Im2 ~~  Im9   0.381 -0.022  -0.022   -0.033   -0.033
## 258   Im21 ~~ Im11   0.373 -0.023  -0.023   -0.030   -0.030
## 259   Im16 ~~ Im18   0.357 -0.021  -0.021   -0.030   -0.030
## 260    Im5 ~~ Im15   0.339 -0.019  -0.019   -0.028   -0.028
## 261   Im21 ~~ Im13   0.328 -0.018  -0.018   -0.034   -0.034
## 262   QUAL =~  Im8   0.320 -0.031  -0.022   -0.021   -0.021
## 263    Im5 ~~ Im21   0.319 -0.021  -0.021   -0.028   -0.028
## 264   DECO =~  Im8   0.317  0.016   0.020    0.019    0.019
## 265    Im7 ~~ Im19   0.317  0.022   0.022    0.026    0.026
## 266    Im4 ~~ Im20   0.315  0.012   0.012    0.047    0.047
## 267   Im11 ~~  Im2   0.310  0.015   0.015    0.030    0.030
## 268    Im5 ~~  Im8   0.298 -0.015  -0.015   -0.026   -0.026
## 269    Im7 ~~ Im20   0.292 -0.021  -0.021   -0.029   -0.029
## 270    Im4 ~~ Im13   0.275 -0.009  -0.009   -0.045   -0.045
## 271    Im3 ~~ Im13   0.274  0.010   0.010    0.033    0.033
## 272    Im8 ~~ Im13   0.252 -0.012  -0.012   -0.028   -0.028
## 273   DECO =~ Im11   0.240  0.019   0.024    0.021    0.021
## 274   Im12 ~~ Im19   0.218  0.013   0.013    0.027    0.027
## 275    Im4 ~~  Im5   0.193  0.017   0.017    0.059    0.059
## 276    Im3 ~~  Im7   0.193 -0.010  -0.010   -0.024   -0.024
## 277    Im7 ~~ Im12   0.191 -0.013  -0.013   -0.025   -0.025
## 278    Im5 ~~ Im17   0.190  0.011   0.011    0.033    0.033
## 279    Im7 ~~ Im21   0.188 -0.017  -0.017   -0.022   -0.022
## 280    Im5 ~~  Im9   0.179  0.020   0.020    0.019    0.019
## 281   Im19 ~~ Im18   0.174 -0.013  -0.013   -0.021   -0.021
## 282   Im21 ~~ Im16   0.170 -0.017  -0.017   -0.020   -0.020
## 283 FRENCH =~  Im4   0.152 -0.018  -0.012   -0.009   -0.009
## 284    Im4 ~~ Im15   0.151 -0.008  -0.008   -0.028   -0.028
## 285   Im21 ~~ Im19   0.149 -0.014  -0.014   -0.019   -0.019
## 286   DECO =~ Im14   0.132 -0.007  -0.008   -0.009   -0.009
## 287    Im4 ~~  Im1   0.125  0.005   0.005    0.033    0.033
## 288    Im3 ~~  Im2   0.124  0.006   0.006    0.022    0.022
## 289    Im2 ~~ Im17   0.116  0.006   0.006    0.031    0.031
## 290   Im10 ~~ Im15   0.108 -0.005  -0.005   -0.018   -0.018
## 291    Im5 ~~ Im10   0.106 -0.006  -0.006   -0.018   -0.018
## 292 FRENCH =~ Im21   0.106  0.023   0.015    0.011    0.011
## 293    Im6 ~~ Im16   0.097 -0.014  -0.014   -0.014   -0.014
## 294 CHOICE =~  Im8   0.094 -0.009  -0.011   -0.010   -0.010
## 295    Im7 ~~ Im11   0.091 -0.012  -0.012   -0.014   -0.014
## 296   Im10 ~~ Im21   0.089 -0.005  -0.005   -0.018   -0.018
## 297   Im11 ~~ Im18   0.089  0.010   0.010    0.015    0.015
## 298    Im5 ~~  Im2   0.087 -0.008  -0.008   -0.016   -0.016
## 299    Im7 ~~ Im18   0.086 -0.010  -0.010   -0.015   -0.015
## 300   QUAL =~  Im6   0.086 -0.023  -0.016   -0.013   -0.013
## 301    Im5 ~~ Im12   0.084  0.008   0.008    0.017    0.017
## 302 CHOICE =~ Im11   0.082 -0.012  -0.015   -0.013   -0.013
## 303    Im8 ~~ Im12   0.076 -0.006  -0.006   -0.016   -0.016
## 304    Im6 ~~ Im13   0.071  0.009   0.009    0.014    0.014
## 305   Im14 ~~ Im20   0.068 -0.004  -0.004   -0.018   -0.018
## 306    Im5 ~~  Im7   0.064  0.010   0.010    0.012    0.012
## 307   Im22 ~~ Im17   0.054  0.006   0.006    0.022    0.022
## 308    Im6 ~~ Im21   0.052 -0.010  -0.010   -0.011   -0.011
## 309   QUAL =~ Im21   0.051  0.016   0.011    0.008    0.008
## 310    Im4 ~~ Im21   0.046  0.005   0.005    0.017    0.017
## 311   Im21 ~~ Im15   0.040 -0.007  -0.007   -0.010   -0.010
## 312   Im14 ~~ Im12   0.039 -0.003  -0.003   -0.015   -0.015
## 313    Im7 ~~ Im13   0.037 -0.006  -0.006   -0.011   -0.011
## 314    Im8 ~~ Im17   0.036 -0.004  -0.004   -0.015   -0.015
## 315   QUAL =~ Im17   0.035 -0.015  -0.011   -0.009   -0.009
## 316  BRAND =~ Im21   0.027 -0.007  -0.009   -0.006   -0.006
## 317   Im14 ~~ Im19   0.027  0.003   0.003    0.010    0.010
## 318   Im20 ~~  Im9   0.021  0.007   0.007    0.008    0.008
## 319    Im7 ~~ Im17   0.021 -0.004  -0.004   -0.011   -0.011
## 320  BRAND =~  Im8   0.020  0.004   0.005    0.005    0.005
## 321 CHOICE =~  Im3   0.018 -0.004  -0.004   -0.003   -0.003
## 322    Im3 ~~  Im9   0.018 -0.004  -0.004   -0.007   -0.007
## 323    Im5 ~~ Im18   0.017  0.004   0.004    0.007    0.007
## 324   DECO =~ Im21   0.017  0.005   0.006    0.005    0.005
## 325    Im8 ~~ Im20   0.014  0.003   0.003    0.006    0.006
## 326    Im4 ~~  Im9   0.014 -0.003  -0.003   -0.008   -0.008
## 327    Im3 ~~ Im21   0.010 -0.002  -0.002   -0.006   -0.006
## 328  ATMOS =~ Im18   0.009  0.004   0.005    0.004    0.004
## 329   Im11 ~~ Im15   0.007 -0.003  -0.003   -0.004   -0.004
## 330    Im7 ~~  Im2   0.006 -0.002  -0.002   -0.004   -0.004
## 331 FRENCH =~ Im12   0.002 -0.003  -0.002   -0.002   -0.002
## 332   Im13 ~~  Im9   0.002  0.002   0.002    0.003    0.003
## 333    Im4 ~~ Im14   0.002  0.000   0.000   -0.004   -0.004
## 334    Im4 ~~  Im7   0.002 -0.001  -0.001   -0.003   -0.003
## 335    Im8 ~~ Im11   0.002  0.001   0.001    0.002    0.002
## 336   Im13 ~~ Im19   0.002  0.001   0.001    0.002    0.002
## 337    Im3 ~~  Im6   0.002  0.001   0.001    0.002    0.002
## 338   Im22 ~~ Im16   0.001  0.001   0.001    0.002    0.002
## 339   QUAL =~  Im3   0.001  0.001   0.001    0.001    0.001
## 340    Im6 ~~ Im17   0.000  0.000   0.000   -0.001   -0.001
## 341    Im5 ~~ Im13   0.000  0.000   0.000    0.000    0.000

2.3.2 7 factor model

Based on the modification indices we create a new model

# # no excluded variables:
# CFA_model_img_7f <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7 + Im9
# "

# MIs indicate separate Im1, Im2 and Im16, Im19 no excluded variables
# Im8 under FRENCH
# exclude Im8 
# exclude Im15
# exclude Im9
CFA_model_img_7f <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2  
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7
"

# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "

# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "

# # 8 factor model: excluded variables: Im9, Im15, Im8, Im11
# CFA_model_img_7f <- "
# QUAL =~ Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# PROF =~ Im16 + Im19
# "


CFA_fit_img_7f <- cfa(CFA_model_img_7f, data=survey, missing="ML")
summary(CFA_fit_img_7f, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6.15 ended normally after 108 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        85
## 
##   Number of observations                           553
##   Number of missing patterns                        79
## 
## Model Test User Model:
##                                                       
##   Test statistic                               259.047
##   Degrees of freedom                               124
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                              7474.765
##   Degrees of freedom                               171
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.982
##   Tucker-Lewis Index (TLI)                       0.975
##                                                       
##   Robust Comparative Fit Index (CFI)             0.981
##   Robust Tucker-Lewis Index (TLI)                0.974
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -12973.111
##   Loglikelihood unrestricted model (H1)     -12843.588
##                                                       
##   Akaike (AIC)                               26116.223
##   Bayesian (BIC)                             26483.028
##   Sample-size adjusted Bayesian (SABIC)      26213.200
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.044
##   90 Percent confidence interval - lower         0.037
##   90 Percent confidence interval - upper         0.052
##   P-value H_0: RMSEA <= 0.050                    0.886
##   P-value H_0: RMSEA >= 0.080                    0.000
##                                                       
##   Robust RMSEA                                   0.045
##   90 Percent confidence interval - lower         0.038
##   90 Percent confidence interval - upper         0.053
##   P-value H_0: Robust RMSEA <= 0.050             0.825
##   P-value H_0: Robust RMSEA >= 0.080             0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.029
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.236    0.937
##     Im4               1.056    0.025   42.717    0.000    1.305    0.969
##     Im5               0.818    0.034   23.815    0.000    1.011    0.760
##   FOOD =~                                                               
##     Im10              1.000                               0.812    0.923
##     Im14              1.015    0.036   28.479    0.000    0.824    0.952
##   ATMOS =~                                                              
##     Im20              1.000                               1.265    0.845
##     Im21              0.849    0.041   20.823    0.000    1.074    0.783
##     Im22              1.060    0.047   22.606    0.000    1.340    0.877
##   PRODQUAL =~                                                           
##     Im11              1.000                               0.703    0.615
##     Im12              1.410    0.094   15.046    0.000    0.991    0.872
##     Im13              1.465    0.105   13.968    0.000    1.030    0.855
##   CHOICE =~                                                             
##     Im1               1.000                               1.305    0.980
##     Im2               0.885    0.033   27.043    0.000    1.155    0.899
##   PROF =~                                                               
##     Im16              1.000                               0.921    0.766
##     Im19              1.046    0.061   17.170    0.000    0.963    0.856
##   BRAND =~                                                              
##     Im17              1.000                               1.204    0.969
##     Im18              0.994    0.041   24.143    0.000    1.197    0.856
##   FRENCH =~                                                             
##     Im6               1.000                               0.975    0.813
##     Im7               1.184    0.071   16.770    0.000    1.155    0.955
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FOOD              0.418    0.050    8.393    0.000    0.416    0.416
##     ATMOS             0.730    0.082    8.912    0.000    0.467    0.467
##     PRODQUAL          0.409    0.051    8.040    0.000    0.471    0.471
##     CHOICE            0.711    0.079    9.032    0.000    0.441    0.441
##     PROF              0.743    0.071   10.465    0.000    0.653    0.653
##     BRAND             0.770    0.076   10.140    0.000    0.517    0.517
##     FRENCH            0.402    0.063    6.350    0.000    0.334    0.334
##   FOOD ~~                                                               
##     ATMOS             0.303    0.051    5.948    0.000    0.295    0.295
##     PRODQUAL          0.258    0.034    7.662    0.000    0.452    0.452
##     CHOICE            0.328    0.050    6.584    0.000    0.309    0.309
##     PROF              0.372    0.043    8.589    0.000    0.498    0.498
##     BRAND             0.318    0.047    6.801    0.000    0.325    0.325
##     FRENCH            0.463    0.047    9.829    0.000    0.585    0.585
##   ATMOS ~~                                                              
##     PRODQUAL          0.372    0.053    7.011    0.000    0.418    0.418
##     CHOICE            0.739    0.085    8.728    0.000    0.448    0.448
##     PROF              0.557    0.069    8.089    0.000    0.478    0.478
##     BRAND             0.787    0.081    9.715    0.000    0.516    0.516
##     FRENCH            0.410    0.065    6.352    0.000    0.333    0.333
##   PRODQUAL ~~                                                           
##     CHOICE            0.439    0.054    8.161    0.000    0.478    0.478
##     PROF              0.343    0.043    7.946    0.000    0.529    0.529
##     BRAND             0.479    0.053    9.046    0.000    0.566    0.566
##     FRENCH            0.210    0.037    5.622    0.000    0.306    0.306
##   CHOICE ~~                                                             
##     PROF              0.717    0.072    9.956    0.000    0.597    0.597
##     BRAND             0.817    0.079   10.362    0.000    0.519    0.519
##     FRENCH            0.286    0.060    4.735    0.000    0.225    0.225
##   PROF ~~                                                               
##     BRAND             0.667    0.066   10.040    0.000    0.601    0.601
##     FRENCH            0.328    0.051    6.438    0.000    0.366    0.366
##   BRAND ~~                                                              
##     FRENCH            0.378    0.061    6.175    0.000    0.322    0.322
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.995    0.056   88.560    0.000    4.995    3.786
##    .Im4               4.999    0.057   86.983    0.000    4.999    3.712
##    .Im5               5.035    0.057   87.844    0.000    5.035    3.787
##    .Im10              6.100    0.037  162.789    0.000    6.100    6.937
##    .Im14              6.138    0.037  165.861    0.000    6.138    7.093
##    .Im20              4.672    0.064   73.177    0.000    4.672    3.123
##    .Im21              5.139    0.058   87.970    0.000    5.139    3.751
##    .Im22              4.279    0.065   65.401    0.000    4.279    2.799
##    .Im11              5.653    0.049  115.271    0.000    5.653    4.943
##    .Im12              5.666    0.049  116.089    0.000    5.666    4.983
##    .Im13              5.448    0.052  105.615    0.000    5.448    4.524
##    .Im1               4.790    0.057   84.202    0.000    4.790    3.597
##    .Im2               4.857    0.055   88.354    0.000    4.857    3.779
##    .Im16              5.135    0.052   99.147    0.000    5.135    4.269
##    .Im19              5.145    0.048  106.948    0.000    5.145    4.574
##    .Im17              5.025    0.053   94.519    0.000    5.025    4.041
##    .Im18              4.595    0.060   76.447    0.000    4.595    3.287
##    .Im6               5.827    0.051  113.784    0.000    5.827    4.858
##    .Im7               5.753    0.052  110.826    0.000    5.753    4.756
##     DECO              0.000                               0.000    0.000
##     FOOD              0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     PRODQUAL          0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     PROF              0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.213    0.024    8.755    0.000    0.213    0.122
##    .Im4               0.109    0.024    4.532    0.000    0.109    0.060
##    .Im5               0.747    0.049   15.217    0.000    0.747    0.422
##    .Im10              0.114    0.019    5.961    0.000    0.114    0.148
##    .Im14              0.070    0.019    3.680    0.000    0.070    0.093
##    .Im20              0.638    0.061   10.451    0.000    0.638    0.285
##    .Im21              0.725    0.057   12.672    0.000    0.725    0.386
##    .Im22              0.541    0.063    8.539    0.000    0.541    0.231
##    .Im11              0.814    0.055   14.802    0.000    0.814    0.622
##    .Im12              0.310    0.040    7.845    0.000    0.310    0.240
##    .Im13              0.390    0.045    8.765    0.000    0.390    0.269
##    .Im1               0.070    0.050    1.394    0.163    0.070    0.040
##    .Im2               0.317    0.044    7.233    0.000    0.317    0.192
##    .Im16              0.599    0.052   11.498    0.000    0.599    0.414
##    .Im19              0.338    0.045    7.457    0.000    0.338    0.267
##    .Im17              0.095    0.045    2.112    0.035    0.095    0.062
##    .Im18              0.521    0.055    9.540    0.000    0.521    0.267
##    .Im6               0.487    0.056    8.677    0.000    0.487    0.339
##    .Im7               0.128    0.067    1.930    0.054    0.128    0.088
##     DECO              1.528    0.107   14.326    0.000    1.000    1.000
##     FOOD              0.659    0.049   13.328    0.000    1.000    1.000
##     ATMOS             1.599    0.138   11.623    0.000    1.000    1.000
##     PRODQUAL          0.494    0.067    7.361    0.000    1.000    1.000
##     CHOICE            1.704    0.118   14.388    0.000    1.000    1.000
##     PROF              0.849    0.088    9.638    0.000    1.000    1.000
##     BRAND             1.451    0.104   13.988    0.000    1.000    1.000
##     FRENCH            0.952    0.095   10.058    0.000    1.000    1.000

2.3.2.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.3.2.2 local fit measures

# semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5, 
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
         rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
         nCharNodes = 7,shapeMan = "rectangle", 
         sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
         curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
         )

lambda = inspect(CFA_fit_img_7f, what="std")$lambda
theta = inspect(CFA_fit_img_7f, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones
2.3.2.2.1 Indicator reliability criterion
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail
##      DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## Im3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im4   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im5   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im10  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im14  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im20  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im21  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im22  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im11  NaN  NaN   NaN  0.378    NaN  NaN   NaN    NaN
## Im12  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im13  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im2   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im16  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im19  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im17  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im18  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im6   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im7   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
2.3.2.2.2 Construct reliability criterion
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
2.3.2.2.3 Average Variance Extracted criterion
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
2.3.2.2.4 Fornell-Larcker Criteria
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_7f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail
##          DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO        1                                           
## FOOD      NaN    1                                      
## ATMOS     NaN  NaN     1                                
## PRODQUAL  NaN  NaN   NaN      1                         
## CHOICE    NaN  NaN   NaN    NaN      1                  
## PROF      NaN  NaN   NaN    NaN    NaN    1             
## BRAND     NaN  NaN   NaN    NaN    NaN  NaN     1       
## FRENCH    NaN  NaN   NaN    NaN    NaN  NaN   NaN      1
# AVE should be higher than squared correlations between constructs

# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full
##               DECO      FOOD     ATMOS PRODQUAL    CHOICE      PROF     BRAND
## DECO     0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FOOD     0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## ATMOS    0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PRODQUAL 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## CHOICE   0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PROF     0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## BRAND    0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FRENCH   0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
##            FRENCH
## DECO     0.786707
## FOOD     0.786707
## ATMOS    0.786707
## PRODQUAL 0.786707
## CHOICE   0.786707
## PROF     0.786707
## BRAND    0.786707
## FRENCH   0.786707
psi
##           DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH
## DECO     1.000                                             
## FOOD     0.416 1.000                                       
## ATMOS    0.467 0.295 1.000                                 
## PRODQUAL 0.471 0.452 0.418  1.000                          
## CHOICE   0.441 0.309 0.448  0.478  1.000                   
## PROF     0.653 0.498 0.478  0.529  0.597 1.000             
## BRAND    0.517 0.325 0.516  0.566  0.519 0.601 1.000       
## FRENCH   0.334 0.585 0.333  0.306  0.225 0.366 0.322  1.000
AVEpsi_fail
##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH
## DECO          .                                                 
## FOOD        NaN      .                                          
## ATMOS       NaN    NaN      .                                   
## PRODQUAL    NaN    NaN    NaN      .                            
## CHOICE      NaN    NaN    NaN    NaN      .                     
## PROF        NaN    NaN    NaN    NaN    NaN      .              
## BRAND       NaN    NaN    NaN    NaN    NaN    NaN      .       
## FRENCH      NaN    NaN    NaN    NaN    NaN    NaN    NaN      .

2.3.2.3 Modification indices

arrange(modificationindices(CFA_fit_img_7f),-mi)
##          lhs op  rhs     mi    epc sepc.lv sepc.all sepc.nox
## 1      BRAND =~ Im13 23.832  0.220   0.265    0.220    0.220
## 2       Im11 ~~ Im13 21.323 -0.191  -0.191   -0.338   -0.338
## 3      BRAND =~ Im12 17.245 -0.179  -0.216   -0.190   -0.190
## 4       Im21 ~~ Im22 15.139 -0.285  -0.285   -0.455   -0.455
## 5     CHOICE =~ Im20 14.777 -0.151  -0.197   -0.132   -0.132
## 6     CHOICE =~ Im13 13.970  0.133   0.174    0.144    0.144
## 7       Im11 ~~ Im12 13.307  0.145   0.145    0.288    0.288
## 8       FOOD =~ Im11 12.742  0.215   0.174    0.152    0.152
## 9       Im20 ~~ Im21 11.455  0.228   0.228    0.335    0.335
## 10     ATMOS =~ Im12 10.952 -0.115  -0.145   -0.127   -0.127
## 11      Im13 ~~  Im1 10.707  0.068   0.068    0.409    0.409
## 12    CHOICE =~ Im12 10.663 -0.111  -0.145   -0.127   -0.127
## 13      Im13 ~~ Im17  9.392  0.068   0.068    0.355    0.355
## 14       Im4 ~~ Im17  9.096 -0.046  -0.046   -0.446   -0.446
## 15     BRAND =~ Im20  8.230 -0.133  -0.160   -0.107   -0.107
## 16      Im10 ~~ Im16  7.956  0.046   0.046    0.175    0.175
## 17     BRAND =~ Im22  7.656  0.131   0.158    0.103    0.103
## 18    FRENCH =~ Im22  7.278  0.136   0.132    0.087    0.087
## 19     ATMOS =~ Im11  6.691  0.101   0.128    0.112    0.112
## 20      Im22 ~~ Im12  6.644 -0.076  -0.076   -0.185   -0.185
## 21    CHOICE =~  Im5  6.302  0.086   0.112    0.084    0.084
## 22     BRAND =~  Im4  6.247 -0.067  -0.081   -0.060   -0.060
## 23  PRODQUAL =~  Im5  6.120  0.171   0.120    0.091    0.091
## 24      Im14 ~~ Im16  6.048 -0.039  -0.039   -0.191   -0.191
## 25      Im10 ~~  Im6  6.011 -0.035  -0.035   -0.147   -0.147
## 26     BRAND =~  Im5  5.755  0.095   0.115    0.086    0.086
## 27       Im3 ~~  Im1  5.614 -0.034  -0.034   -0.281   -0.281
## 28      DECO =~  Im7  5.531 -0.093  -0.114   -0.095   -0.095
## 29      DECO =~  Im6  5.531  0.078   0.097    0.080    0.080
## 30     ATMOS =~  Im5  5.517  0.089   0.113    0.085    0.085
## 31      DECO =~ Im18  5.361  0.099   0.123    0.088    0.088
## 32      DECO =~ Im17  5.361 -0.100  -0.124   -0.099   -0.099
## 33    FRENCH =~ Im20  5.231 -0.113  -0.111   -0.074   -0.074
## 34      Im22 ~~ Im11  5.182  0.087   0.087    0.131    0.131
## 35      FOOD =~ Im13  5.137 -0.127  -0.103   -0.086   -0.086
## 36       Im3 ~~  Im4  5.131  0.162   0.162    1.061    1.061
## 37      DECO =~ Im20  5.124 -0.096  -0.118   -0.079   -0.079
## 38     BRAND =~  Im7  5.064 -0.090  -0.108   -0.089   -0.089
## 39     BRAND =~  Im6  5.064  0.076   0.091    0.076    0.076
## 40      Im22 ~~  Im1  5.051  0.056   0.056    0.290    0.290
## 41      Im13 ~~ Im16  5.040 -0.067  -0.067   -0.138   -0.138
## 42      Im11 ~~  Im6  4.965 -0.069  -0.069   -0.109   -0.109
## 43      Im10 ~~ Im13  4.793 -0.031  -0.031   -0.146   -0.146
## 44       Im4 ~~ Im18  4.776  0.040   0.040    0.166    0.166
## 45       Im5 ~~  Im6  4.758 -0.065  -0.065   -0.108   -0.108
## 46       Im3 ~~ Im22  4.749  0.049   0.049    0.143    0.143
## 47      Im10 ~~  Im7  4.706  0.032   0.032    0.265    0.265
## 48    CHOICE =~ Im22  4.697  0.087   0.113    0.074    0.074
## 49       Im3 ~~  Im5  4.674 -0.071  -0.071   -0.178   -0.178
## 50      Im13 ~~  Im2  4.562 -0.044  -0.044   -0.125   -0.125
## 51      FOOD =~  Im5  4.520  0.117   0.095    0.072    0.072
## 52      Im20 ~~ Im17  4.488 -0.057  -0.057   -0.230   -0.230
## 53     ATMOS =~  Im4  4.309 -0.052  -0.066   -0.049   -0.049
## 54      DECO =~ Im22  4.302  0.090   0.111    0.072    0.072
## 55      PROF =~  Im2  4.223  0.170   0.157    0.122    0.122
## 56      PROF =~  Im1  4.223 -0.192  -0.177   -0.133   -0.133
## 57      Im20 ~~  Im6  4.215 -0.064  -0.064   -0.115   -0.115
## 58  PRODQUAL =~  Im1  4.027  0.145   0.102    0.077    0.077
## 59  PRODQUAL =~  Im2  4.027 -0.129  -0.090   -0.070   -0.070
## 60      PROF =~ Im12  3.965 -0.117  -0.108   -0.095   -0.095
## 61      Im14 ~~  Im6  3.823  0.027   0.027    0.149    0.149
## 62      FOOD =~  Im6  3.804 -0.271  -0.220   -0.183   -0.183
## 63      FOOD =~  Im7  3.804  0.321   0.260    0.215    0.215
## 64       Im2 ~~ Im17  3.691  0.033   0.033    0.192    0.192
## 65       Im4 ~~  Im6  3.588  0.033   0.033    0.143    0.143
## 66       Im3 ~~ Im17  3.342  0.028   0.028    0.198    0.198
## 67      Im11 ~~  Im1  3.335 -0.045  -0.045   -0.189   -0.189
## 68       Im5 ~~  Im1  3.275  0.043   0.043    0.188    0.188
## 69      PROF =~ Im20  3.209 -0.113  -0.104   -0.069   -0.069
## 70    CHOICE =~ Im21  3.202  0.067   0.087    0.064    0.064
## 71       Im3 ~~  Im2  3.151  0.026   0.026    0.100    0.100
## 72      Im20 ~~ Im13  3.089  0.055   0.055    0.111    0.111
## 73      Im18 ~~  Im6  3.067  0.046   0.046    0.091    0.091
## 74      Im14 ~~  Im7  3.014 -0.026  -0.026   -0.272   -0.272
## 75      Im11 ~~ Im17  2.983 -0.045  -0.045   -0.163   -0.163
## 76    FRENCH =~ Im11  2.967  0.080   0.078    0.069    0.069
## 77     ATMOS =~ Im13  2.904  0.062   0.078    0.065    0.065
## 78       Im5 ~~  Im7  2.807  0.048   0.048    0.154    0.154
## 79      Im10 ~~ Im11  2.784  0.028   0.028    0.093    0.093
## 80      Im20 ~~  Im1  2.774 -0.042  -0.042   -0.198   -0.198
## 81       Im5 ~~ Im14  2.721  0.026   0.026    0.115    0.115
## 82       Im1 ~~ Im17  2.656 -0.029  -0.029   -0.359   -0.359
## 83    FRENCH =~ Im19  2.578  0.085   0.083    0.074    0.074
## 84    FRENCH =~ Im16  2.578 -0.082  -0.080   -0.066   -0.066
## 85       Im2 ~~ Im16  2.577  0.038   0.038    0.088    0.088
## 86    CHOICE =~ Im14  2.577  0.027   0.035    0.041    0.041
## 87    CHOICE =~ Im10  2.577 -0.026  -0.035   -0.039   -0.039
## 88      Im21 ~~ Im18  2.573 -0.052  -0.052   -0.084   -0.084
## 89       Im4 ~~ Im11  2.457 -0.034  -0.034   -0.113   -0.113
## 90      PROF =~ Im13  2.455  0.096   0.089    0.074    0.074
## 91      Im22 ~~ Im19  2.419 -0.049  -0.049   -0.115   -0.115
## 92       Im4 ~~ Im22  2.418 -0.034  -0.034   -0.138   -0.138
## 93       Im3 ~~ Im20  2.350 -0.034  -0.034   -0.093   -0.093
## 94      Im12 ~~  Im7  2.333  0.036   0.036    0.178    0.178
## 95      DECO =~ Im12  2.244 -0.054  -0.066   -0.058   -0.058
## 96      Im11 ~~  Im7  2.221  0.044   0.044    0.137    0.137
## 97      Im19 ~~ Im17  2.187  0.035   0.035    0.193    0.193
## 98  PRODQUAL =~ Im16  2.157 -0.133  -0.094   -0.078   -0.078
## 99  PRODQUAL =~ Im19  2.157  0.140   0.098    0.087    0.087
## 100     Im10 ~~ Im17  2.035 -0.017  -0.017   -0.161   -0.161
## 101     Im14 ~~ Im17  1.988  0.016   0.016    0.201    0.201
## 102      Im4 ~~  Im1  1.978  0.020   0.020    0.227    0.227
## 103      Im3 ~~ Im12  1.906 -0.024  -0.024   -0.092   -0.092
## 104     Im12 ~~  Im6  1.902 -0.033  -0.033   -0.084   -0.084
## 105   CHOICE =~ Im16  1.817  0.068   0.089    0.074    0.074
## 106   CHOICE =~ Im19  1.817 -0.071  -0.093   -0.083   -0.083
## 107     Im14 ~~  Im2  1.800  0.015   0.015    0.098    0.098
## 108     Im18 ~~  Im7  1.743 -0.033  -0.033   -0.128   -0.128
## 109   FRENCH =~  Im5  1.735  0.059   0.057    0.043    0.043
## 110     Im11 ~~  Im2  1.713  0.033   0.033    0.064    0.064
## 111    ATMOS =~ Im17  1.684 -0.057  -0.073   -0.058   -0.058
## 112    ATMOS =~ Im18  1.684  0.057   0.072    0.052    0.052
## 113     Im19 ~~ Im18  1.680 -0.034  -0.034   -0.082   -0.082
## 114    BRAND =~  Im3  1.663  0.034   0.041    0.031    0.031
## 115      Im3 ~~ Im14  1.662 -0.012  -0.012   -0.102   -0.102
## 116   FRENCH =~  Im2  1.647  0.039   0.038    0.030    0.030
## 117   FRENCH =~  Im1  1.647 -0.045  -0.043   -0.033   -0.033
## 118     Im22 ~~  Im2  1.646 -0.032  -0.032   -0.077   -0.077
## 119     Im22 ~~ Im18  1.613  0.041   0.041    0.077    0.077
## 120     FOOD =~  Im2  1.604  0.050   0.040    0.031    0.031
## 121     FOOD =~  Im1  1.604 -0.056  -0.046   -0.034   -0.034
## 122 PRODQUAL =~  Im4  1.602 -0.058  -0.041   -0.030   -0.030
## 123     Im22 ~~ Im13  1.588 -0.040  -0.040   -0.086   -0.086
## 124      Im4 ~~  Im2  1.557 -0.018  -0.018   -0.095   -0.095
## 125     Im14 ~~ Im21  1.552  0.021   0.021    0.091    0.091
## 126      Im5 ~~ Im16  1.529 -0.043  -0.043   -0.064   -0.064
## 127     Im12 ~~ Im17  1.526 -0.026  -0.026   -0.151   -0.151
## 128     Im10 ~~ Im18  1.519  0.018   0.018    0.072    0.072
## 129 PRODQUAL =~ Im22  1.519 -0.095  -0.067   -0.044   -0.044
## 130      Im2 ~~ Im18  1.481 -0.026  -0.026   -0.063   -0.063
## 131     Im12 ~~ Im13  1.475  0.089   0.089    0.257    0.257
## 132 PRODQUAL =~  Im6  1.473 -0.073  -0.052   -0.043   -0.043
## 133 PRODQUAL =~  Im7  1.473  0.087   0.061    0.051    0.051
## 134     Im14 ~~ Im18  1.464 -0.017  -0.017   -0.088   -0.088
## 135     PROF =~ Im22  1.445  0.077   0.071    0.047    0.047
## 136     DECO =~ Im13  1.431  0.045   0.055    0.046    0.046
## 137 PRODQUAL =~ Im17  1.422  0.109   0.076    0.062    0.062
## 138 PRODQUAL =~ Im18  1.422 -0.108  -0.076   -0.054   -0.054
## 139      Im4 ~~ Im12  1.373  0.019   0.019    0.106    0.106
## 140    ATMOS =~  Im1  1.355  0.043   0.054    0.040    0.040
## 141    ATMOS =~  Im2  1.355 -0.038  -0.048   -0.037   -0.037
## 142     Im22 ~~  Im7  1.342  0.035   0.035    0.133    0.133
## 143      Im3 ~~ Im18  1.316 -0.022  -0.022   -0.065   -0.065
## 144      Im3 ~~ Im11  1.290  0.025   0.025    0.061    0.061
## 145     PROF =~  Im4  1.267 -0.055  -0.050   -0.037   -0.037
## 146     Im13 ~~ Im19  1.244  0.029   0.029    0.080    0.080
## 147      Im3 ~~ Im10  1.231  0.011   0.011    0.071    0.071
## 148     Im10 ~~ Im12  1.205  0.014   0.014    0.077    0.077
## 149     Im12 ~~ Im16  1.199  0.030   0.030    0.071    0.071
## 150    BRAND =~ Im11  1.070 -0.047  -0.056   -0.049   -0.049
## 151    BRAND =~  Im2  1.067  0.042   0.051    0.039    0.039
## 152    BRAND =~  Im1  1.067 -0.048  -0.057   -0.043   -0.043
## 153     Im14 ~~ Im12  1.061 -0.013  -0.013   -0.090   -0.090
## 154      Im4 ~~  Im7  1.054 -0.017  -0.017   -0.147   -0.147
## 155 PRODQUAL =~ Im20  1.037  0.077   0.054    0.036    0.036
## 156     Im21 ~~ Im17  1.017  0.027   0.027    0.101    0.101
## 157     Im20 ~~ Im19  0.988  0.031   0.031    0.068    0.068
## 158     PROF =~ Im17  0.986  0.084   0.077    0.062    0.062
## 159     PROF =~ Im18  0.986 -0.083  -0.077   -0.055   -0.055
## 160     Im19 ~~  Im7  0.949  0.025   0.025    0.122    0.122
## 161     PROF =~  Im7  0.940 -0.060  -0.055   -0.045   -0.045
## 162     PROF =~  Im6  0.940  0.050   0.046    0.039    0.039
## 163     Im13 ~~ Im18  0.925 -0.026  -0.026   -0.057   -0.057
## 164      Im5 ~~  Im2  0.918 -0.023  -0.023   -0.047   -0.047
## 165     Im14 ~~ Im13  0.889  0.013   0.013    0.079    0.079
## 166     Im16 ~~  Im7  0.880 -0.027  -0.027   -0.097   -0.097
## 167      Im1 ~~ Im18  0.847  0.019   0.019    0.101    0.101
## 168    ATMOS =~  Im3  0.826  0.022   0.028    0.022    0.022
## 169     FOOD =~ Im20  0.814 -0.052  -0.042   -0.028   -0.028
## 170     Im22 ~~  Im6  0.806  0.028   0.028    0.054    0.054
## 171      Im5 ~~ Im19  0.786 -0.026  -0.026   -0.052   -0.052
## 172    BRAND =~ Im16  0.775 -0.050  -0.060   -0.050   -0.050
## 173    BRAND =~ Im19  0.775  0.052   0.063    0.056    0.056
## 174      Im3 ~~ Im19  0.774  0.016   0.016    0.061    0.061
## 175    BRAND =~ Im14  0.773  0.017   0.020    0.023    0.023
## 176    BRAND =~ Im10  0.773 -0.016  -0.020   -0.022   -0.022
## 177     Im10 ~~ Im19  0.726 -0.012  -0.012   -0.062   -0.062
## 178   FRENCH =~ Im13  0.706 -0.035  -0.034   -0.028   -0.028
## 179     PROF =~  Im5  0.688  0.055   0.051    0.038    0.038
## 180      Im4 ~~  Im5  0.687  0.029   0.029    0.103    0.103
## 181     Im20 ~~ Im12  0.675  0.024   0.024    0.054    0.054
## 182      Im2 ~~  Im7  0.669  0.016   0.016    0.079    0.079
## 183      Im3 ~~  Im7  0.637 -0.014  -0.014   -0.084   -0.084
## 184 PRODQUAL =~ Im14  0.619  0.031   0.022    0.025    0.025
## 185 PRODQUAL =~ Im10  0.619 -0.030  -0.021   -0.024   -0.024
## 186     Im21 ~~  Im7  0.611 -0.023  -0.023   -0.076   -0.076
## 187      Im5 ~~ Im22  0.596  0.028   0.028    0.044    0.044
## 188      Im4 ~~ Im10  0.595 -0.007  -0.007   -0.066   -0.066
## 189     Im20 ~~ Im18  0.582  0.025   0.025    0.043    0.043
## 190     Im10 ~~  Im2  0.581 -0.008  -0.008   -0.045   -0.045
## 191      Im4 ~~ Im16  0.579  0.016   0.016    0.062    0.062
## 192     Im21 ~~  Im2  0.574  0.019   0.019    0.039    0.039
## 193     Im10 ~~ Im21  0.544 -0.013  -0.013   -0.043   -0.043
## 194     Im14 ~~ Im22  0.525 -0.012  -0.012   -0.062   -0.062
## 195     Im13 ~~  Im7  0.518 -0.018  -0.018   -0.080   -0.080
## 196      Im5 ~~ Im11  0.501  0.026   0.026    0.033    0.033
## 197     Im20 ~~ Im11  0.498  0.027   0.027    0.038    0.038
## 198     Im12 ~~  Im2  0.492 -0.013  -0.013   -0.043   -0.043
## 199     Im11 ~~ Im18  0.492  0.023   0.023    0.035    0.035
## 200   CHOICE =~  Im3  0.483 -0.015  -0.020   -0.015   -0.015
## 201      Im1 ~~ Im16  0.483 -0.017  -0.017   -0.082   -0.082
## 202     Im21 ~~ Im12  0.479  0.020   0.020    0.043    0.043
## 203      Im5 ~~ Im10  0.474 -0.011  -0.011   -0.039   -0.039
## 204   CHOICE =~ Im11  0.473 -0.026  -0.034   -0.030   -0.030
## 205     Im10 ~~ Im20  0.466  0.012   0.012    0.043    0.043
## 206     PROF =~  Im3  0.453  0.032   0.029    0.022    0.022
## 207   FRENCH =~  Im3  0.431 -0.019  -0.018   -0.014   -0.014
## 208     FOOD =~  Im3  0.430 -0.023  -0.019   -0.014   -0.014
## 209     FOOD =~ Im19  0.429  0.047   0.038    0.034    0.034
## 210     FOOD =~ Im16  0.429 -0.045  -0.037   -0.031   -0.031
## 211     PROF =~ Im11  0.410  0.039   0.036    0.032    0.032
## 212      Im5 ~~ Im20  0.382  0.023   0.023    0.033    0.033
## 213     Im13 ~~  Im6  0.377  0.016   0.016    0.036    0.036
## 214     Im14 ~~ Im19  0.372  0.009   0.009    0.056    0.056
## 215     Im21 ~~ Im13  0.372 -0.019  -0.019   -0.036   -0.036
## 216     PROF =~ Im21  0.371  0.036   0.033    0.024    0.024
## 217   CHOICE =~  Im4  0.369 -0.014  -0.018   -0.013   -0.013
## 218     Im22 ~~ Im17  0.360  0.016   0.016    0.071    0.071
## 219   FRENCH =~ Im21  0.360 -0.029  -0.028   -0.020   -0.020
## 220     Im21 ~~ Im11  0.346 -0.022  -0.022   -0.029   -0.029
## 221      Im5 ~~ Im17  0.345  0.015   0.015    0.055    0.055
## 222     Im14 ~~ Im20  0.330 -0.010  -0.010   -0.045   -0.045
## 223     FOOD =~ Im21  0.320  0.032   0.026    0.019    0.019
## 224   CHOICE =~ Im17  0.309  0.023   0.030    0.024    0.024
## 225   CHOICE =~ Im18  0.309 -0.023  -0.030   -0.021   -0.021
## 226      Im3 ~~ Im13  0.299  0.010   0.010    0.035    0.035
## 227      Im4 ~~ Im19  0.281 -0.010  -0.010   -0.050   -0.050
## 228     Im22 ~~ Im16  0.277  0.019   0.019    0.033    0.033
## 229      Im5 ~~ Im21  0.277 -0.019  -0.019   -0.026   -0.026
## 230      Im4 ~~ Im14  0.246  0.005   0.005    0.053    0.053
## 231     DECO =~ Im11  0.238  0.019   0.024    0.021    0.021
## 232     Im16 ~~ Im18  0.231 -0.015  -0.015   -0.026   -0.026
## 233     Im17 ~~  Im7  0.228 -0.010  -0.010   -0.094   -0.094
## 234     Im21 ~~ Im16  0.227 -0.017  -0.017   -0.026   -0.026
## 235     Im20 ~~ Im22  0.211  0.043   0.043    0.074    0.074
## 236     Im17 ~~  Im6  0.208  0.010   0.010    0.045    0.045
## 237     Im20 ~~  Im2  0.203 -0.011  -0.011   -0.025   -0.025
## 238      Im2 ~~ Im19  0.202 -0.009  -0.009   -0.029   -0.029
## 239     FOOD =~  Im4  0.194 -0.016  -0.013   -0.010   -0.010
## 240      Im4 ~~ Im13  0.168 -0.007  -0.007   -0.035   -0.035
## 241     Im14 ~~ Im11  0.165  0.007   0.007    0.028    0.028
## 242     FOOD =~ Im22  0.151  0.023   0.018    0.012    0.012
## 243     Im12 ~~ Im18  0.146 -0.010  -0.010   -0.024   -0.024
## 244     Im20 ~~ Im16  0.145  0.014   0.014    0.022    0.022
## 245     Im21 ~~  Im1  0.132  0.009   0.009    0.040    0.040
## 246    ATMOS =~ Im19  0.131 -0.017  -0.022   -0.019   -0.019
## 247    ATMOS =~ Im16  0.131  0.016   0.021    0.017    0.017
## 248      Im4 ~~ Im20  0.129  0.008   0.008    0.029    0.029
## 249      Im1 ~~  Im7  0.126 -0.007  -0.007   -0.075   -0.075
## 250     Im12 ~~  Im1  0.110 -0.006  -0.006   -0.044   -0.044
## 251      Im3 ~~  Im6  0.106  0.006   0.006    0.018    0.018
## 252      Im2 ~~  Im6  0.094 -0.006  -0.006   -0.016   -0.016
## 253   FRENCH =~ Im18  0.094  0.013   0.012    0.009    0.009
## 254   FRENCH =~ Im17  0.094 -0.013  -0.013   -0.010   -0.010
## 255     Im10 ~~  Im1  0.093 -0.003  -0.003   -0.038   -0.038
## 256 PRODQUAL =~ Im21  0.088  0.021   0.015    0.011    0.011
## 257      Im5 ~~ Im18  0.083  0.009   0.009    0.014    0.014
## 258     Im20 ~~  Im7  0.082  0.009   0.009    0.030    0.030
## 259     DECO =~  Im2  0.075  0.009   0.011    0.008    0.008
## 260     DECO =~  Im1  0.075 -0.010  -0.012   -0.009   -0.009
## 261      Im5 ~~ Im12  0.067  0.007   0.007    0.015    0.015
## 262     Im14 ~~  Im1  0.063 -0.003  -0.003   -0.039   -0.039
## 263    ATMOS =~ Im14  0.061  0.004   0.006    0.006    0.006
## 264    ATMOS =~ Im10  0.061 -0.004  -0.006   -0.006   -0.006
## 265     Im21 ~~ Im19  0.060  0.008   0.008    0.015    0.015
## 266      Im4 ~~ Im21  0.059  0.005   0.005    0.018    0.018
## 267     PROF =~ Im10  0.058  0.008   0.007    0.008    0.008
## 268     PROF =~ Im14  0.058 -0.008  -0.007   -0.009   -0.009
## 269      Im1 ~~ Im19  0.056 -0.005  -0.005   -0.034   -0.034
## 270   CHOICE =~  Im6  0.055 -0.007  -0.009   -0.007   -0.007
## 271   CHOICE =~  Im7  0.055  0.008   0.010    0.008    0.008
## 272     DECO =~ Im14  0.052  0.005   0.006    0.007    0.007
## 273     DECO =~ Im10  0.052 -0.005  -0.006   -0.006   -0.006
## 274     Im10 ~~ Im22  0.051  0.004   0.004    0.015    0.015
## 275   FRENCH =~ Im12  0.045 -0.008  -0.008   -0.007   -0.007
## 276      Im1 ~~  Im6  0.039 -0.004  -0.004   -0.021   -0.021
## 277    ATMOS =~  Im6  0.036 -0.006  -0.008   -0.007   -0.007
## 278    ATMOS =~  Im7  0.036  0.008   0.010    0.008    0.008
## 279     Im12 ~~ Im19  0.023 -0.004  -0.004   -0.011   -0.011
## 280     DECO =~ Im21  0.016  0.005   0.006    0.005    0.005
## 281     FOOD =~ Im17  0.015  0.006   0.005    0.004    0.004
## 282     FOOD =~ Im18  0.015 -0.006  -0.005   -0.004   -0.004
## 283      Im3 ~~ Im21  0.013 -0.003  -0.003   -0.006   -0.006
## 284     Im16 ~~  Im6  0.011 -0.003  -0.003   -0.006   -0.006
## 285     Im19 ~~  Im6  0.009 -0.002  -0.002   -0.006   -0.006
## 286     Im11 ~~ Im19  0.006 -0.002  -0.002   -0.005   -0.005
## 287     Im21 ~~  Im6  0.006  0.002   0.002    0.004    0.004
## 288     DECO =~ Im16  0.004  0.004   0.005    0.004    0.004
## 289     DECO =~ Im19  0.004 -0.004  -0.005   -0.004   -0.004
## 290     Im11 ~~ Im16  0.002  0.002   0.002    0.002    0.002
## 291   FRENCH =~ Im14  0.001  0.001   0.001    0.002    0.002
## 292   FRENCH =~ Im10  0.001 -0.001  -0.001   -0.002   -0.002
## 293      Im3 ~~ Im16  0.001 -0.001  -0.001   -0.002   -0.002
## 294   FRENCH =~  Im4  0.001 -0.001  -0.001    0.000    0.000
## 295     Im16 ~~ Im17  0.000  0.000   0.000    0.002    0.002
## 296 PRODQUAL =~  Im3  0.000  0.000   0.000    0.000    0.000
## 297      Im5 ~~ Im13  0.000  0.000   0.000    0.000    0.000
## 298    BRAND =~ Im21  0.000  0.000   0.000    0.000    0.000
## 299     FOOD =~ Im12  0.000  0.000   0.000    0.000    0.000

2.4 SEM

## don't actually think we need this as we can use the full data for confirmatory and path analysis
# data_img_EFA2
# data.frame(EFA_PAFn[[3]]$scores)
# 
# numcol_data_img_EFA = dim(data_img_EFA2)[2]
# numcol_scores = dim(EFA_PAFn[[3]]$scores)[2]
# numcol_data_img_EFA
# numcol_scores
# 
# CFA_data = cbind(data_img_EFA2, EFA_PAFn[[3]]$scores, survey_excl_img2["SAT_1"])
# CFA_data
# # colnames(CFA_data)[23:29] = c("Gourmet food", "Brand image", "Choice range", "Relaxed atmosphere", "Decoration", "Product quality", "Frenchness")
# 
# # colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO")
# colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO", "QUAL", "FRENCH")
# 
# CFA_data

2.4.1 model images to mediators

# missing Im8, Im15, Im9

# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2  
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# 
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
# 
# SAT ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# AFCOM ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# "

# delete relationships based on regression significance levels
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2  
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7

AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4

SAT ~ DECO + CHOICE + PROF
AFCOM ~ ATMOS + PRODQUAL + FRENCH
"

2.4.2 linear regression

# # linear regression
# lm_SAT_1 <-  lm (model_SAT_1, data = survey) 
# summary(lm_SAT_1)
# # note: lm deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.3 path analysis

# path analysis
SEM_fit <- cfa(model_SEM, data=survey, missing="ML")
summary(SEM_fit, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6.15 ended normally after 143 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       148
## 
##   Number of observations                           553
##   Number of missing patterns                       135
## 
## Model Test User Model:
##                                                       
##   Test statistic                               807.817
##   Degrees of freedom                               412
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             11978.557
##   Degrees of freedom                               496
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.966
##   Tucker-Lewis Index (TLI)                       0.959
##                                                       
##   Robust Comparative Fit Index (CFI)             0.966
##   Robust Tucker-Lewis Index (TLI)                0.959
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -22422.581
##   Loglikelihood unrestricted model (H1)     -22018.673
##                                                       
##   Akaike (AIC)                               45141.162
##   Bayesian (BIC)                             45779.835
##   Sample-size adjusted Bayesian (SABIC)      45310.018
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.042
##   90 Percent confidence interval - lower         0.037
##   90 Percent confidence interval - upper         0.046
##   P-value H_0: RMSEA <= 0.050                    0.999
##   P-value H_0: RMSEA >= 0.080                    0.000
##                                                       
##   Robust RMSEA                                   0.042
##   90 Percent confidence interval - lower         0.038
##   90 Percent confidence interval - upper         0.047
##   P-value H_0: Robust RMSEA <= 0.050             0.998
##   P-value H_0: Robust RMSEA >= 0.080             0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.059
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.235    0.936
##     Im4               1.057    0.025   42.676    0.000    1.306    0.970
##     Im5               0.818    0.034   23.801    0.000    1.010    0.760
##   FOOD =~                                                               
##     Im10              1.000                               0.810    0.921
##     Im14              1.019    0.036   28.596    0.000    0.826    0.954
##   ATMOS =~                                                              
##     Im20              1.000                               1.253    0.838
##     Im21              0.865    0.041   20.940    0.000    1.084    0.791
##     Im22              1.060    0.046   23.188    0.000    1.327    0.869
##   PRODQUAL =~                                                           
##     Im11              1.000                               0.703    0.615
##     Im12              1.409    0.094   15.045    0.000    0.991    0.872
##     Im13              1.464    0.105   13.957    0.000    1.029    0.855
##   CHOICE =~                                                             
##     Im1               1.000                               1.302    0.978
##     Im2               0.889    0.032   27.907    0.000    1.157    0.900
##   PROF =~                                                               
##     Im16              1.000                               0.911    0.757
##     Im19              1.030    0.056   18.278    0.000    0.938    0.834
##   BRAND =~                                                              
##     Im17              1.000                               1.205    0.970
##     Im18              0.992    0.041   24.147    0.000    1.196    0.856
##   FRENCH =~                                                             
##     Im6               1.000                               0.986    0.822
##     Im7               1.161    0.066   17.619    0.000    1.144    0.945
##   AFCOM =~                                                              
##     COM_A1            1.000                               1.120    0.785
##     COM_A2            1.180    0.056   21.211    0.000    1.321    0.830
##     COM_A3            1.176    0.059   19.829    0.000    1.317    0.816
##     COM_A4            1.297    0.063   20.613    0.000    1.453    0.845
##   SAT =~                                                                
##     SAT_1             1.000                               0.868    0.859
##     SAT_2             0.937    0.049   19.036    0.000    0.814    0.818
##     SAT_3             0.812    0.055   14.799    0.000    0.705    0.620
##   RI =~                                                                 
##     C_REP1            1.000                               0.588    0.798
##     C_REP2            1.021    0.047   21.905    0.000    0.601    0.955
##     C_REP3            0.719    0.038   19.135    0.000    0.423    0.758
##   COI =~                                                                
##     C_CR1             1.000                               1.641    0.848
##     C_CR3             1.033    0.051   20.134    0.000    1.695    0.822
##     C_CR4             0.967    0.049   19.687    0.000    1.587    0.805
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   SAT ~                                                                 
##     DECO             -0.107    0.046   -2.357    0.018   -0.153   -0.153
##     CHOICE            0.095    0.040    2.379    0.017    0.142    0.142
##     PROF              0.615    0.090    6.808    0.000    0.645    0.645
##   AFCOM ~                                                               
##     ATMOS             0.437    0.047    9.282    0.000    0.489    0.489
##     PRODQUAL         -0.037    0.076   -0.485    0.628   -0.023   -0.023
##     FRENCH            0.206    0.051    4.031    0.000    0.182    0.182
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FOOD              0.416    0.050    8.380    0.000    0.416    0.416
##     ATMOS             0.730    0.081    8.972    0.000    0.472    0.472
##     PRODQUAL          0.408    0.051    8.031    0.000    0.470    0.470
##     CHOICE            0.709    0.079    9.024    0.000    0.441    0.441
##     PROF              0.750    0.070   10.690    0.000    0.667    0.667
##     BRAND             0.768    0.076   10.124    0.000    0.516    0.516
##     FRENCH            0.412    0.063    6.494    0.000    0.338    0.338
##     RI                0.181    0.035    5.193    0.000    0.249    0.249
##     COI               0.047    0.095    0.492    0.623    0.023    0.023
##   FOOD ~~                                                               
##     ATMOS             0.303    0.050    6.019    0.000    0.299    0.299
##     PRODQUAL          0.257    0.034    7.652    0.000    0.452    0.452
##     CHOICE            0.328    0.050    6.606    0.000    0.311    0.311
##     PROF              0.387    0.043    8.999    0.000    0.525    0.525
##     BRAND             0.317    0.047    6.798    0.000    0.325    0.325
##     FRENCH            0.469    0.047   10.016    0.000    0.588    0.588
##     RI                0.123    0.023    5.283    0.000    0.258    0.258
##     COI              -0.044    0.063   -0.700    0.484   -0.033   -0.033
##   ATMOS ~~                                                              
##     PRODQUAL          0.370    0.053    7.026    0.000    0.420    0.420
##     CHOICE            0.748    0.084    8.879    0.000    0.458    0.458
##     PROF              0.580    0.068    8.542    0.000    0.508    0.508
##     BRAND             0.785    0.080    9.748    0.000    0.520    0.520
##     FRENCH            0.411    0.065    6.374    0.000    0.333    0.333
##     RI                0.281    0.040    7.034    0.000    0.381    0.381
##     COI               0.436    0.103    4.210    0.000    0.212    0.212
##   PRODQUAL ~~                                                           
##     CHOICE            0.437    0.054    8.146    0.000    0.477    0.477
##     PROF              0.348    0.043    8.092    0.000    0.543    0.543
##     BRAND             0.479    0.053    9.046    0.000    0.566    0.566
##     FRENCH            0.211    0.038    5.621    0.000    0.305    0.305
##     RI                0.112    0.022    5.128    0.000    0.270    0.270
##     COI               0.060    0.058    1.036    0.300    0.052    0.052
##   CHOICE ~~                                                             
##     PROF              0.725    0.071   10.200    0.000    0.611    0.611
##     BRAND             0.816    0.079   10.366    0.000    0.520    0.520
##     FRENCH            0.296    0.061    4.829    0.000    0.231    0.231
##     RI                0.216    0.037    5.829    0.000    0.282    0.282
##     COI               0.068    0.100    0.678    0.498    0.032    0.032
##   PROF ~~                                                               
##     BRAND             0.676    0.065   10.326    0.000    0.616    0.616
##     FRENCH            0.363    0.052    6.990    0.000    0.404    0.404
##     RI                0.200    0.030    6.678    0.000    0.373    0.373
##     COI              -0.079    0.077   -1.029    0.304   -0.053   -0.053
##   BRAND ~~                                                              
##     FRENCH            0.388    0.061    6.333    0.000    0.327    0.327
##     RI                0.188    0.034    5.501    0.000    0.265    0.265
##     COI               0.111    0.094    1.190    0.234    0.056    0.056
##   FRENCH ~~                                                             
##     RI                0.134    0.029    4.535    0.000    0.230    0.230
##     COI               0.004    0.078    0.051    0.959    0.002    0.002
##   RI ~~                                                                 
##     COI               0.078    0.047    1.677    0.094    0.081    0.081
##  .AFCOM ~~                                                              
##    .SAT               0.218    0.037    5.825    0.000    0.357    0.357
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.995    0.056   88.576    0.000    4.995    3.787
##    .Im4               4.999    0.057   86.999    0.000    4.999    3.713
##    .Im5               5.036    0.057   87.853    0.000    5.036    3.787
##    .Im10              6.100    0.037  162.781    0.000    6.100    6.936
##    .Im14              6.138    0.037  165.851    0.000    6.138    7.093
##    .Im20              4.672    0.064   73.228    0.000    4.672    3.125
##    .Im21              5.139    0.058   87.975    0.000    5.139    3.750
##    .Im22              4.280    0.065   65.485    0.000    4.280    2.802
##    .Im11              5.654    0.049  115.283    0.000    5.654    4.943
##    .Im12              5.666    0.049  116.116    0.000    5.666    4.985
##    .Im13              5.448    0.052  105.654    0.000    5.448    4.526
##    .Im1               4.792    0.057   84.287    0.000    4.792    3.600
##    .Im2               4.858    0.055   88.415    0.000    4.858    3.781
##    .Im16              5.135    0.052   99.179    0.000    5.135    4.269
##    .Im19              5.146    0.048  107.001    0.000    5.146    4.575
##    .Im17              5.025    0.053   94.560    0.000    5.025    4.043
##    .Im18              4.595    0.060   76.466    0.000    4.595    3.288
##    .Im6               5.827    0.051  113.792    0.000    5.827    4.858
##    .Im7               5.753    0.052  110.790    0.000    5.753    4.754
##    .COM_A1            4.287    0.061   70.288    0.000    4.287    3.007
##    .COM_A2            3.887    0.068   57.199    0.000    3.887    2.443
##    .COM_A3            3.542    0.069   51.223    0.000    3.542    2.194
##    .COM_A4            3.458    0.073   47.108    0.000    3.458    2.010
##    .SAT_1             5.343    0.043  124.118    0.000    5.343    5.289
##    .SAT_2             5.483    0.042  129.018    0.000    5.483    5.510
##    .SAT_3             5.458    0.050  109.971    0.000    5.458    4.798
##    .C_REP1            4.283    0.031  136.277    0.000    4.283    5.807
##    .C_REP2            4.507    0.027  167.674    0.000    4.507    7.164
##    .C_REP3            4.676    0.024  195.449    0.000    4.676    8.380
##    .C_CR1             2.679    0.083   32.285    0.000    2.679    1.384
##    .C_CR3             3.261    0.088   37.105    0.000    3.261    1.582
##    .C_CR4             2.786    0.084   33.092    0.000    2.786    1.414
##     DECO              0.000                               0.000    0.000
##     FOOD              0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     PRODQUAL          0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     PROF              0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
##    .AFCOM             0.000                               0.000    0.000
##    .SAT               0.000                               0.000    0.000
##     RI                0.000                               0.000    0.000
##     COI               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.214    0.024    8.767    0.000    0.214    0.123
##    .Im4               0.108    0.024    4.461    0.000    0.108    0.059
##    .Im5               0.747    0.049   15.220    0.000    0.747    0.423
##    .Im10              0.117    0.019    6.135    0.000    0.117    0.151
##    .Im14              0.067    0.019    3.559    0.000    0.067    0.089
##    .Im20              0.666    0.059   11.280    0.000    0.666    0.298
##    .Im21              0.703    0.055   12.679    0.000    0.703    0.374
##    .Im22              0.571    0.060    9.496    0.000    0.571    0.245
##    .Im11              0.814    0.055   14.788    0.000    0.814    0.622
##    .Im12              0.310    0.040    7.841    0.000    0.310    0.240
##    .Im13              0.390    0.045    8.730    0.000    0.390    0.269
##    .Im1               0.076    0.048    1.598    0.110    0.076    0.043
##    .Im2               0.312    0.042    7.417    0.000    0.312    0.189
##    .Im16              0.618    0.051   12.116    0.000    0.618    0.427
##    .Im19              0.385    0.045    8.653    0.000    0.385    0.304
##    .Im17              0.093    0.045    2.055    0.040    0.093    0.060
##    .Im18              0.524    0.055    9.587    0.000    0.524    0.268
##    .Im6               0.468    0.054    8.714    0.000    0.468    0.325
##    .Im7               0.155    0.062    2.520    0.012    0.155    0.106
##    .COM_A1            0.779    0.060   13.036    0.000    0.779    0.383
##    .COM_A2            0.787    0.067   11.838    0.000    0.787    0.311
##    .COM_A3            0.872    0.070   12.387    0.000    0.872    0.335
##    .COM_A4            0.849    0.075   11.385    0.000    0.849    0.287
##    .SAT_1             0.267    0.034    7.920    0.000    0.267    0.262
##    .SAT_2             0.328    0.033    9.901    0.000    0.328    0.331
##    .SAT_3             0.797    0.056   14.318    0.000    0.797    0.616
##    .C_REP1            0.198    0.016   12.178    0.000    0.198    0.364
##    .C_REP2            0.035    0.011    3.224    0.001    0.035    0.089
##    .C_REP3            0.133    0.009   14.064    0.000    0.133    0.426
##    .C_CR1             1.054    0.114    9.275    0.000    1.054    0.281
##    .C_CR3             1.375    0.131   10.514    0.000    1.375    0.324
##    .C_CR4             1.366    0.123   11.130    0.000    1.366    0.352
##     DECO              1.526    0.107   14.317    0.000    1.000    1.000
##     FOOD              0.657    0.049   13.302    0.000    1.000    1.000
##     ATMOS             1.569    0.135   11.580    0.000    1.000    1.000
##     PRODQUAL          0.494    0.067    7.362    0.000    1.000    1.000
##     CHOICE            1.696    0.117   14.476    0.000    1.000    1.000
##     PROF              0.829    0.086    9.605    0.000    1.000    1.000
##     BRAND             1.452    0.104   14.014    0.000    1.000    1.000
##     FRENCH            0.971    0.094   10.349    0.000    1.000    1.000
##    .AFCOM             0.854    0.086    9.878    0.000    0.681    0.681
##    .SAT               0.436    0.050    8.755    0.000    0.579    0.579
##     RI                0.346    0.032   10.668    0.000    1.000    1.000
##     COI               2.693    0.238   11.334    0.000    1.000    1.000
# note: cfa deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.3.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.4.3.2 local fit measures

# semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5, 
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
         rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
         nCharNodes = 7,shapeMan = "rectangle", 
         sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
         curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
         )

lambda = inspect(SEM_fit, what="std")$lambda
theta = inspect(SEM_fit, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones
2.4.3.2.1 Indicator reliability criterion
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail
##        DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM   SAT  RI COI
## Im3     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im4     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im5     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im10    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im14    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im20    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im21    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im22    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im11    NaN  NaN   NaN  0.378    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im12    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im13    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im1     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im2     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im16    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im19    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im17    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im18    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im6     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im7     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A4  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## SAT_1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## SAT_2   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## SAT_3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN 0.384 NaN NaN
## C_REP1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_REP2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_REP3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_CR1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_CR3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_CR4   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
2.4.3.2.2 Construct reliability criterion
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
2.4.3.2.3 Average Variance Extracted criterion
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
2.4.3.2.4 Fornell-Larcker Criteria
# correlations between constructs (factors...) should be lower than .7
psi = inspect(SEM_fit, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail
##          DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO        1                                                             
## FOOD      NaN    1                                                        
## ATMOS     NaN  NaN     1                                                  
## PRODQUAL  NaN  NaN   NaN      1                                           
## CHOICE    NaN  NaN   NaN    NaN      1                                    
## PROF      NaN  NaN   NaN    NaN    NaN    1                               
## BRAND     NaN  NaN   NaN    NaN    NaN  NaN     1                         
## FRENCH    NaN  NaN   NaN    NaN    NaN  NaN   NaN      1                  
## AFCOM     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN            
## SAT       NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN        
## RI        NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN   1    
## COI       NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN   1
# AVE should be higher than squared correlations between constructs

# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full
##               DECO      FOOD     ATMOS  PRODQUAL    CHOICE      PROF     BRAND
## DECO     0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FOOD     0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## ATMOS    0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## PRODQUAL 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## CHOICE   0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## PROF     0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## BRAND    0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FRENCH   0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## AFCOM    0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## SAT      0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## RI       0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## COI      0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
##             FRENCH     AFCOM       SAT        RI       COI
## DECO     0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## FOOD     0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## ATMOS    0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## PRODQUAL 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## CHOICE   0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## PROF     0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## BRAND    0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## FRENCH   0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## AFCOM    0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## SAT      0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## RI       0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## COI      0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
psi
##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH  AFCOM    SAT
## DECO      1.000                                                               
## FOOD      0.416  1.000                                                        
## ATMOS     0.472  0.299  1.000                                                 
## PRODQUAL  0.470  0.452  0.420  1.000                                          
## CHOICE    0.441  0.311  0.458  0.477  1.000                                   
## PROF      0.667  0.525  0.508  0.543  0.611  1.000                            
## BRAND     0.516  0.325  0.520  0.566  0.520  0.616  1.000                     
## FRENCH    0.338  0.588  0.333  0.305  0.231  0.404  0.327  1.000              
## AFCOM     0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.681       
## SAT       0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.357  0.579
## RI        0.249  0.258  0.381  0.270  0.282  0.373  0.265  0.230  0.000  0.000
## COI       0.023 -0.033  0.212  0.052  0.032 -0.053  0.056  0.002  0.000  0.000
##              RI    COI
## DECO                  
## FOOD                  
## ATMOS                 
## PRODQUAL              
## CHOICE                
## PROF                  
## BRAND                 
## FRENCH                
## AFCOM                 
## SAT                   
## RI        1.000       
## COI       0.081  1.000
AVEpsi_fail
##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH  AFCOM    SAT
## DECO          .                                                               
## FOOD        NaN      .                                                        
## ATMOS       NaN    NaN      .                                                 
## PRODQUAL    NaN    NaN    NaN      .                                          
## CHOICE      NaN    NaN    NaN    NaN      .                                   
## PROF        NaN    NaN    NaN    NaN    NaN      .                            
## BRAND       NaN    NaN    NaN    NaN    NaN    NaN      .                     
## FRENCH      NaN    NaN    NaN    NaN    NaN    NaN    NaN      .              
## AFCOM       NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .       
## SAT         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .
## RI          NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## COI         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
##              RI    COI
## DECO                  
## FOOD                  
## ATMOS                 
## PRODQUAL              
## CHOICE                
## PROF                  
## BRAND                 
## FRENCH                
## AFCOM                 
## SAT                   
## RI            .       
## COI         NaN      .

2.4.3.3 Modification indices

arrange(modificationindices(SEM_fit),-mi)
##          lhs op      rhs     mi    epc sepc.lv sepc.all sepc.nox
## 1      AFCOM =~   C_REP1 61.877  0.158   0.177    0.240    0.240
## 2      ATMOS ~~    AFCOM 49.054 -0.587  -0.507   -0.507   -0.507
## 3      ATMOS  ~    AFCOM 35.588 -0.540  -0.483   -0.483   -0.483
## 4      AFCOM ~~       RI 32.373  0.134   0.247    0.247    0.247
## 5     COM_A1 ~~   COM_A2 31.301  0.288   0.288    0.368    0.368
## 6      AFCOM ~~      COI 31.255  0.406   0.268    0.268    0.268
## 7      ATMOS =~   C_REP1 26.283  0.102   0.127    0.173    0.173
## 8       Im16 ~~     Im19 25.773  0.371   0.371    0.761    0.761
## 9       PROF ~~      SAT 25.773 -0.222  -0.368   -0.368   -0.368
## 10     BRAND =~     Im13 23.807  0.219   0.264    0.219    0.219
## 11    C_REP2 ~~   C_REP3 23.244  0.096   0.096    1.407    1.407
## 12       SAT ~~       RI 22.140  0.089   0.229    0.229    0.229
## 13      Im11 ~~     Im13 21.621 -0.192  -0.192   -0.341   -0.341
## 14       SAT =~   C_REP1 18.223  0.115   0.099    0.135    0.135
## 15        RI =~    SAT_2 17.895  0.232   0.137    0.137    0.137
## 16     BRAND =~     Im12 17.152 -0.178  -0.214   -0.189   -0.189
## 17    CHOICE =~     Im20 16.326 -0.160  -0.208   -0.139   -0.139
## 18        RI =~     Im22 15.906 -0.338  -0.199   -0.130   -0.130
## 19        RI =~   COM_A1 15.392  0.299   0.176    0.123    0.123
## 20      PROF  ~      SAT 14.568 -0.337  -0.322   -0.322   -0.322
## 21    CHOICE =~     Im13 14.137  0.134   0.175    0.145    0.145
## 22      Im11 ~~     Im12 13.137  0.144   0.144    0.286    0.286
## 23    COM_A3 ~~   C_REP1 13.055  0.078   0.078    0.188    0.188
## 24      FOOD =~     Im11 12.685  0.215   0.174    0.152    0.152
## 25     AFCOM =~     Im11 11.893  0.138   0.154    0.135    0.135
## 26    CHOICE =~   C_REP1 11.775  0.059   0.077    0.104    0.104
## 27       SAT  ~   FRENCH 11.592  0.143   0.163    0.163    0.163
## 28  PRODQUAL =~    C_CR4 11.365  0.307   0.216    0.109    0.109
## 29      PROF =~   COM_A3 11.354  0.198   0.180    0.112    0.112
## 30      Im21 ~~   C_REP3 11.319  0.052   0.052    0.171    0.171
## 31     ATMOS =~     Im12 11.112 -0.116  -0.146   -0.128   -0.128
## 32     AFCOM =~     Im20 10.705 -0.168  -0.188   -0.126   -0.126
## 33    FRENCH =~   C_REP1 10.658  0.075   0.074    0.100    0.100
## 34    CHOICE =~     Im12 10.534 -0.111  -0.144   -0.127   -0.127
## 35      Im21 ~~     Im22 10.334 -0.190  -0.190   -0.299   -0.299
## 36      Im13 ~~      Im1 10.251  0.066   0.066    0.382    0.382
## 37  PRODQUAL ~~    AFCOM  9.881 -0.142  -0.219   -0.219   -0.219
## 38      DECO =~   C_REP1  9.764  0.056   0.069    0.094    0.094
## 39     AFCOM  ~   CHOICE  9.453  0.130   0.151    0.151    0.151
## 40       SAT =~   COM_A2  9.449 -0.194  -0.168   -0.106   -0.106
## 41      Im13 ~~     Im17  9.292  0.068   0.068    0.358    0.358
## 42       SAT =~   COM_A3  9.262  0.199   0.173    0.107    0.107
## 43     AFCOM  ~      SAT  9.120  0.359   0.278    0.278    0.278
## 44       Im4 ~~     Im17  9.042 -0.045  -0.045   -0.453   -0.453
## 45       Im1 ~~    SAT_2  9.041 -0.055  -0.055   -0.346   -0.346
## 46  PRODQUAL  ~    AFCOM  8.849 -0.148  -0.235   -0.235   -0.235
## 47       SAT  ~    AFCOM  8.555  0.220   0.284    0.284    0.284
## 48      Im20 ~~     Im22  8.506  0.205   0.205    0.333    0.333
## 49      Im10 ~~     Im16  8.198  0.046   0.046    0.173    0.173
## 50       SAT =~     Im12  8.068 -0.129  -0.112   -0.099   -0.099
## 51     ATMOS =~     Im11  7.837  0.111   0.138    0.121    0.121
## 52     AFCOM =~     Im12  7.657 -0.091  -0.102   -0.090   -0.090
## 53      Im14 ~~     Im16  7.416 -0.043  -0.043   -0.212   -0.212
## 54      Im20 ~~     Im21  7.388  0.150   0.150    0.219    0.219
## 55  PRODQUAL =~    C_CR1  7.333 -0.237  -0.166   -0.086   -0.086
## 56    FRENCH =~     Im22  7.319  0.137   0.135    0.088    0.088
## 57       COI =~   C_REP1  7.224  0.036   0.060    0.081    0.081
## 58     ATMOS =~    C_CR4  7.213  0.140   0.176    0.089    0.089
## 59      Im10 ~~   COM_A2  7.207  0.049   0.049    0.162    0.162
## 60      DECO =~   COM_A3  7.153  0.107   0.132    0.082    0.082
## 61     BRAND =~     Im20  7.150 -0.123  -0.148   -0.099   -0.099
## 62      FOOD =~   C_REP1  7.149  0.074   0.060    0.081    0.081
## 63    CHOICE =~   C_REP3  7.114 -0.037  -0.048   -0.086   -0.086
## 64       SAT =~    C_CR4  7.053  0.194   0.169    0.086    0.086
## 65    COM_A1 ~~   COM_A4  7.039 -0.148  -0.148   -0.183   -0.183
## 66    FRENCH =~   C_REP2  7.027 -0.050  -0.050   -0.079   -0.079
## 67     ATMOS =~   C_REP3  6.995 -0.042  -0.053   -0.094   -0.094
## 68     AFCOM  ~     PROF  6.907  0.199   0.162    0.162    0.162
## 69     BRAND =~     Im22  6.898  0.122   0.148    0.097    0.097
## 70       SAT ~~      COI  6.822 -0.152  -0.140   -0.140   -0.140
## 71      Im19 ~~   C_REP1  6.618 -0.040  -0.040   -0.145   -0.145
## 72        RI =~     Im16  6.453 -0.207  -0.122   -0.101   -0.101
## 73      Im10 ~~      Im6  6.414 -0.036  -0.036   -0.152   -0.152
## 74    FRENCH =~     Im16  6.315 -0.127  -0.126   -0.104   -0.104
## 75    CHOICE =~      Im5  6.298  0.086   0.112    0.085    0.085
## 76     BRAND =~      Im4  6.287 -0.067  -0.081   -0.060   -0.060
## 77      PROF =~     Im12  6.238 -0.152  -0.138   -0.122   -0.122
## 78  PRODQUAL =~      Im5  6.228  0.173   0.121    0.091    0.091
## 79     BRAND =~    C_CR4  6.197  0.127   0.153    0.078    0.078
## 80      PROF =~   C_REP1  6.135  0.069   0.062    0.085    0.085
## 81      Im22 ~~      Im1  6.117  0.062   0.062    0.296    0.296
## 82     ATMOS =~      Im5  6.069  0.095   0.119    0.089    0.089
## 83    C_REP1 ~~   C_REP2  6.068 -0.076  -0.076   -0.909   -0.909
## 84     SAT_2 ~~    SAT_3  6.011 -0.090  -0.090   -0.177   -0.177
## 85      DECO =~    C_CR4  5.821  0.119   0.147    0.075    0.075
## 86     BRAND =~      Im5  5.807  0.096   0.115    0.087    0.087
## 87      FOOD =~      Im6  5.787 -0.269  -0.218   -0.182   -0.182
## 88     BRAND =~   COM_A3  5.704  0.099   0.120    0.074    0.074
## 89      PROF =~    C_CR4  5.642  0.168   0.153    0.078    0.078
## 90      Im13 ~~     Im16  5.612 -0.070  -0.070   -0.144   -0.144
## 91      DECO =~     Im18  5.593  0.101   0.125    0.089    0.089
## 92      DECO =~     Im17  5.593 -0.102  -0.126   -0.101   -0.101
## 93     SAT_1 ~~    SAT_3  5.570  0.092   0.092    0.200    0.200
## 94    COM_A3 ~~   COM_A4  5.532  0.152   0.152    0.176    0.176
## 95       Im3 ~~      Im1  5.490 -0.034  -0.034   -0.265   -0.265
## 96      Im10 ~~      Im7  5.466  0.034   0.034    0.252    0.252
## 97    COM_A1 ~~   C_REP2  5.455  0.034   0.034    0.207    0.207
## 98      Im22 ~~     Im12  5.408 -0.068  -0.068   -0.163   -0.163
## 99      Im11 ~~      Im6  5.400 -0.072  -0.072   -0.116   -0.116
## 100    AFCOM =~    C_CR4  5.370  0.129   0.144    0.073    0.073
## 101     Im22 ~~   C_REP2  5.355 -0.033  -0.033   -0.234   -0.234
## 102     Im16 ~~    SAT_1  5.322 -0.061  -0.061   -0.150   -0.150
## 103    ATMOS =~   C_REP2  5.286 -0.039  -0.049   -0.077   -0.077
## 104     FOOD =~   COM_A3  5.281  0.140   0.113    0.070    0.070
## 105      Im1 ~~    SAT_1  5.167  0.041   0.041    0.287    0.287
## 106     DECO =~     Im20  5.076 -0.095  -0.117   -0.079   -0.079
## 107     DECO =~   C_REP3  5.036 -0.032  -0.040   -0.072   -0.072
## 108     FOOD =~     Im13  5.010 -0.125  -0.102   -0.084   -0.084
## 109      Im5 ~~      Im6  5.010 -0.066  -0.066   -0.112   -0.112
## 110     DECO =~    C_CR1  5.008 -0.106  -0.131   -0.068   -0.068
## 111     DECO =~      Im7  4.885 -0.084  -0.104   -0.086   -0.086
## 112     PROF =~   COM_A2  4.882 -0.125  -0.114   -0.071   -0.071
## 113   CHOICE ~~    AFCOM  4.865  0.101   0.084    0.084    0.084
## 114   C_REP1 ~~   C_REP3  4.856 -0.036  -0.036   -0.225   -0.225
## 115      Im4 ~~    C_CR1  4.822 -0.064  -0.064   -0.191   -0.191
## 116      Im4 ~~     Im18  4.818  0.040   0.040    0.168    0.168
## 117     Im10 ~~     Im13  4.805 -0.031  -0.031   -0.145   -0.145
## 118     FOOD =~   C_REP2  4.798 -0.051  -0.041   -0.065   -0.065
## 119     Im13 ~~      Im2  4.787 -0.045  -0.045   -0.129   -0.129
## 120      Im3 ~~     Im22  4.764  0.049   0.049    0.139    0.139
## 121   FRENCH =~     Im20  4.724 -0.109  -0.107   -0.072   -0.072
## 122     FOOD =~      Im5  4.677  0.120   0.097    0.073    0.073
## 123     FOOD =~      Im7  4.663  0.284   0.230    0.190    0.190
## 124     Im22 ~~   C_REP3  4.654 -0.034  -0.034   -0.123   -0.123
## 125     Im20 ~~     Im17  4.627 -0.058  -0.058   -0.233   -0.233
## 126     PROF =~    SAT_2  4.584  0.130   0.118    0.119    0.119
## 127     Im22 ~~    SAT_1  4.558  0.058   0.058    0.148    0.148
## 128     PROF =~   C_REP3  4.558 -0.048  -0.043   -0.078   -0.078
## 129      Im4 ~~   COM_A3  4.540  0.051   0.051    0.168    0.168
## 130    BRAND =~    C_CR1  4.516 -0.104  -0.126   -0.065   -0.065
## 131   CHOICE  ~    AFCOM  4.498  0.114   0.098    0.098    0.098
## 132     Im11 ~~   C_REP1  4.467  0.041   0.041    0.102    0.102
## 133   COM_A1 ~~    SAT_1  4.359 -0.059  -0.059   -0.128   -0.128
## 134      COI =~   COM_A4  4.335  0.063   0.104    0.060    0.060
## 135      Im3 ~~      Im4  4.333  0.148   0.148    0.977    0.977
## 136       RI =~     Im12  4.281 -0.133  -0.078   -0.069   -0.069
## 137      Im3 ~~      Im5  4.266 -0.068  -0.068   -0.169   -0.169
## 138   FRENCH ~~      SAT  4.214  0.060   0.093    0.093    0.093
## 139      COI =~    SAT_1  4.213 -0.039  -0.064   -0.063   -0.063
## 140    BRAND =~      Im7  4.204 -0.079  -0.096   -0.079   -0.079
## 141    AFCOM =~      Im5  4.180  0.079   0.088    0.066    0.066
## 142     DECO =~      Im6  4.175  0.067   0.083    0.069    0.069
## 143       RI =~     Im21  4.151  0.163   0.096    0.070    0.070
## 144    ATMOS =~      Im4  4.122 -0.052  -0.065   -0.048   -0.048
## 145     Im14 ~~   COM_A2  4.095 -0.036  -0.036   -0.156   -0.156
## 146 PRODQUAL =~      Im2  4.068 -0.124  -0.087   -0.068   -0.068
## 147     DECO =~   COM_A2  4.009 -0.077  -0.095   -0.059   -0.059
## 148     Im20 ~~      Im6  3.960 -0.062  -0.062   -0.111   -0.111
## 149   CHOICE =~   COM_A3  3.948  0.074   0.097    0.060    0.060
## 150     PROF =~     Im13  3.914  0.126   0.114    0.095    0.095
## 151      SAT =~    C_CR1  3.891 -0.138  -0.120   -0.062   -0.062
## 152     PROF =~     Im20  3.844 -0.126  -0.115   -0.077   -0.077
## 153    BRAND =~   C_REP3  3.843 -0.029  -0.036   -0.064   -0.064
## 154     Im16 ~~   C_REP3  3.839 -0.029  -0.029   -0.102   -0.102
## 155    BRAND =~      Im6  3.805  0.065   0.079    0.066    0.066
## 156 PRODQUAL =~      Im1  3.759  0.134   0.094    0.071    0.071
## 157      Im7 ~~   C_REP2  3.754 -0.022  -0.022   -0.298   -0.298
## 158     DECO =~     Im22  3.749  0.083   0.102    0.067    0.067
## 159   COM_A4 ~~    C_CR4  3.747  0.121   0.121    0.112    0.112
## 160     FOOD =~    C_CR4  3.740  0.147   0.119    0.060    0.060
## 161      SAT  ~    ATMOS  3.739  0.072   0.104    0.104    0.104
## 162    SAT_3 ~~    C_CR3  3.717 -0.111  -0.111   -0.106   -0.106
## 163      COI =~     Im19  3.711  0.050   0.083    0.073    0.073
## 164   COM_A2 ~~    SAT_2  3.687 -0.057  -0.057   -0.113   -0.113
## 165     Im20 ~~   COM_A4  3.684  0.085   0.085    0.113    0.113
## 166     Im20 ~~     Im13  3.683  0.061   0.061    0.120    0.120
## 167      Im4 ~~      Im6  3.674  0.033   0.033    0.148    0.148
## 168     Im11 ~~      Im1  3.661 -0.047  -0.047   -0.190   -0.190
## 169     Im22 ~~    SAT_2  3.643 -0.053  -0.053   -0.121   -0.121
## 170       RI =~      Im5  3.628  0.136   0.080    0.060    0.060
## 171   COM_A1 ~~   COM_A3  3.553 -0.099  -0.099   -0.120   -0.120
## 172   COM_A2 ~~   COM_A3  3.545 -0.111  -0.111   -0.134   -0.134
## 173    SAT_1 ~~    C_CR1  3.534 -0.069  -0.069   -0.130   -0.130
## 174      Im3 ~~   COM_A4  3.528  0.048   0.048    0.112    0.112
## 175     Im22 ~~     Im11  3.500  0.071   0.071    0.105    0.105
## 176     PROF =~    C_CR1  3.432 -0.126  -0.115   -0.059   -0.059
## 177      Im2 ~~     Im17  3.429  0.032   0.032    0.188    0.188
## 178    ATMOS =~   COM_A4  3.391  0.094   0.118    0.069    0.069
## 179      Im3 ~~     Im17  3.378  0.028   0.028    0.201    0.201
## 180     Im13 ~~   C_REP2  3.372  0.022   0.022    0.185    0.185
## 181     Im22 ~~   C_REP1  3.355  0.035   0.035    0.105    0.105
## 182     PROF =~      Im2  3.355  0.161   0.147    0.114    0.114
## 183     PROF =~      Im1  3.354 -0.181  -0.165   -0.124   -0.124
## 184   C_REP2 ~~    C_CR4  3.348 -0.037  -0.037   -0.171   -0.171
## 185   FRENCH  ~      SAT  3.327  0.124   0.109    0.109    0.109
## 186     Im13 ~~   C_REP1  3.251 -0.029  -0.029   -0.103   -0.103
## 187     Im20 ~~    SAT_2  3.249  0.050   0.050    0.108    0.108
## 188     Im14 ~~      Im6  3.218  0.025   0.025    0.142    0.142
## 189      COI =~   C_REP2  3.212 -0.020  -0.033   -0.052   -0.052
## 190     Im22 ~~   COM_A1  3.204 -0.071  -0.071   -0.106   -0.106
## 191    AFCOM =~   C_REP3  3.175 -0.029  -0.033   -0.058   -0.058
## 192      COI =~     Im11  3.174  0.048   0.078    0.069    0.069
## 193     PROF =~    SAT_1  3.159 -0.113  -0.103   -0.102   -0.102
## 194      Im1 ~~   C_REP3  3.154 -0.018  -0.018   -0.179   -0.179
## 195     Im11 ~~     Im17  3.129 -0.047  -0.047   -0.169   -0.169
## 196   COM_A2 ~~    C_CR1  3.120  0.099   0.099    0.108    0.108
## 197     Im20 ~~   COM_A2  3.119 -0.074  -0.074   -0.102   -0.102
## 198     Im18 ~~      Im6  3.098  0.046   0.046    0.092    0.092
## 199     Im17 ~~   C_REP1  3.076 -0.023  -0.023   -0.172   -0.172
## 200      Im5 ~~   C_REP1  3.034  0.032   0.032    0.084    0.084
## 201   FRENCH =~     Im11  3.032  0.081   0.080    0.070    0.070
## 202 PRODQUAL =~     Im16  3.000 -0.148  -0.104   -0.087   -0.087
## 203     Im14 ~~    SAT_2  2.981  0.021   0.021    0.139    0.139
## 204 PRODQUAL =~   C_REP3  2.970 -0.046  -0.033   -0.059   -0.059
## 205     Im18 ~~   COM_A1  2.961 -0.057  -0.057   -0.090   -0.090
## 206      Im3 ~~      Im2  2.955  0.025   0.025    0.097    0.097
## 207    BRAND =~   C_REP1  2.929  0.032   0.038    0.052    0.052
## 208   COM_A1 ~~    C_CR3  2.928  0.099   0.099    0.096    0.096
## 209     Im13 ~~   COM_A2  2.909 -0.058  -0.058   -0.104   -0.104
## 210     Im14 ~~      Im7  2.900 -0.025  -0.025   -0.243   -0.243
## 211   COM_A4 ~~    SAT_1  2.891  0.053   0.053    0.111    0.111
## 212   FRENCH =~    C_CR4  2.880  0.108   0.106    0.054    0.054
## 213      Im5 ~~      Im1  2.857  0.040   0.040    0.168    0.168
## 214   FRENCH =~   COM_A3  2.841  0.090   0.089    0.055    0.055
## 215    ATMOS =~   COM_A1  2.817 -0.076  -0.095   -0.067   -0.067
## 216     Im10 ~~     Im11  2.794  0.028   0.028    0.092    0.092
## 217     Im22 ~~      Im2  2.792 -0.042  -0.042   -0.099   -0.099
## 218      SAT =~     Im19  2.751 -0.121  -0.105   -0.093   -0.093
## 219     Im10 ~~    C_CR1  2.731  0.038   0.038    0.109    0.109
## 220     Im14 ~~    C_CR1  2.727 -0.037  -0.037   -0.140   -0.140
## 221    SAT_2 ~~   C_REP1  2.724  0.023   0.023    0.090    0.090
## 222      Im5 ~~     Im14  2.721  0.026   0.026    0.117    0.117
## 223      Im2 ~~    C_CR1  2.710  0.056   0.056    0.098    0.098
## 224       RI =~     Im11  2.694  0.124   0.073    0.064    0.064
## 225      Im5 ~~      Im7  2.692  0.047   0.047    0.137    0.137
## 226   COM_A1 ~~    SAT_3  2.689  0.066   0.066    0.084    0.084
## 227      SAT =~      Im5  2.676  0.086   0.074    0.056    0.056
## 228     Im21 ~~    C_CR3  2.672 -0.091  -0.091   -0.092   -0.092
## 229      Im2 ~~    SAT_2  2.671  0.030   0.030    0.093    0.093
## 230      Im1 ~~     Im17  2.669 -0.029  -0.029   -0.347   -0.347
## 231     Im12 ~~      Im7  2.643  0.038   0.038    0.172    0.172
## 232      SAT =~     Im20  2.596 -0.092  -0.080   -0.053   -0.053
## 233     Im19 ~~    SAT_1  2.588 -0.038  -0.038   -0.117   -0.117
## 234      Im2 ~~     Im16  2.587  0.038   0.038    0.087    0.087
## 235   COM_A2 ~~    SAT_1  2.580 -0.047  -0.047   -0.103   -0.103
## 236     Im20 ~~   COM_A1  2.563 -0.064  -0.064   -0.089   -0.089
## 237   CHOICE =~     Im22  2.551  0.064   0.083    0.054    0.054
## 238    ATMOS =~    C_CR1  2.545 -0.080  -0.100   -0.052   -0.052
## 239    ATMOS =~     Im13  2.531  0.058   0.073    0.061    0.061
## 240   C_REP3 ~~    C_CR3  2.505 -0.037  -0.037   -0.086   -0.086
## 241     Im14 ~~   C_REP3  2.490  0.011   0.011    0.114    0.114
## 242    AFCOM =~    SAT_2  2.425  0.053   0.060    0.060    0.060
## 243      Im2 ~~   C_REP1  2.403  0.020   0.020    0.079    0.079
## 244      Im4 ~~     Im11  2.402 -0.033  -0.033   -0.112   -0.112
## 245      Im3 ~~    C_CR1  2.396  0.047   0.047    0.099    0.099
## 246      Im4 ~~     Im22  2.381 -0.033  -0.033   -0.134   -0.134
## 247   COM_A4 ~~    SAT_3  2.375 -0.069  -0.069   -0.083   -0.083
## 248   CHOICE =~     Im14  2.365  0.026   0.034    0.039    0.039
## 249   CHOICE =~     Im10  2.364 -0.025  -0.033   -0.038   -0.038
## 250      Im5 ~~   COM_A2  2.363  0.061   0.061    0.079    0.079
## 251     FOOD =~    C_CR1  2.363 -0.112  -0.091   -0.047   -0.047
## 252     Im22 ~~    SAT_3  2.338 -0.060  -0.060   -0.088   -0.088
## 253     Im11 ~~   C_REP2  2.334 -0.022  -0.022   -0.128   -0.128
## 254      SAT =~     Im11  2.319  0.084   0.073    0.064    0.064
## 255     FOOD =~    SAT_2  2.311  0.063   0.051    0.052    0.052
## 256     Im20 ~~      Im1  2.293 -0.038  -0.038   -0.169   -0.169
## 257   COM_A4 ~~   C_REP1  2.283  0.033   0.033    0.081    0.081
## 258 PRODQUAL =~    SAT_2  2.262  0.078   0.055    0.055    0.055
## 259   COM_A3 ~~   C_REP2  2.256 -0.024  -0.024   -0.136   -0.136
## 260   COM_A2 ~~   COM_A4  2.244 -0.096  -0.096   -0.118   -0.118
## 261      SAT =~     Im16  2.223 -0.113  -0.098   -0.081   -0.081
## 262   FRENCH =~      Im1  2.216 -0.051  -0.050   -0.038   -0.038
## 263     FOOD =~     Im16  2.214 -0.100  -0.081   -0.067   -0.067
## 264     Im21 ~~     Im18  2.214 -0.047  -0.047   -0.078   -0.078
## 265     Im13 ~~   COM_A3  2.212 -0.052  -0.052   -0.090   -0.090
## 266      SAT =~     Im13  2.196  0.072   0.062    0.052    0.052
## 267      Im2 ~~   C_REP2  2.177 -0.014  -0.014   -0.131   -0.131
## 268     Im22 ~~      Im7  2.176  0.044   0.044    0.149    0.149
## 269     Im19 ~~   COM_A1  2.173  0.047   0.047    0.086    0.086
## 270    AFCOM =~      Im2  2.170  0.041   0.045    0.035    0.035
## 271   COM_A3 ~~   C_REP3  2.156 -0.026  -0.026   -0.076   -0.076
## 272     DECO =~     Im12  2.149 -0.052  -0.065   -0.057   -0.057
## 273      Im5 ~~     Im16  2.143 -0.051  -0.051   -0.074   -0.074
## 274     Im13 ~~    SAT_2  2.137  0.033   0.033    0.092    0.092
## 275   FRENCH =~    SAT_1  2.131  0.048   0.048    0.047    0.047
## 276      Im3 ~~     Im20  2.127 -0.033  -0.033   -0.087   -0.087
## 277      COI =~      Im2  2.123  0.025   0.042    0.032    0.032
## 278      Im4 ~~      Im1  2.121  0.020   0.020    0.226    0.226
## 279      COI =~     Im13  2.103 -0.034  -0.056   -0.046   -0.046
## 280      COI =~   COM_A2  2.066  0.041   0.068    0.043    0.043
## 281      Im3 ~~   COM_A3  2.063 -0.036  -0.036   -0.084   -0.084
## 282    BRAND =~    SAT_2  2.060  0.043   0.052    0.052    0.052
## 283 PRODQUAL =~      Im6  2.054 -0.086  -0.060   -0.050   -0.050
## 284 PRODQUAL =~      Im7  2.054  0.100   0.070    0.058    0.058
## 285     Im22 ~~     Im19  2.047 -0.045  -0.045   -0.095   -0.095
## 286     Im10 ~~     Im17  2.044 -0.017  -0.017   -0.162   -0.162
## 287     Im16 ~~    C_CR4  2.028 -0.074  -0.074   -0.080   -0.080
## 288     Im22 ~~     Im18  2.023  0.046   0.046    0.084    0.084
## 289   FRENCH =~   COM_A2  2.019 -0.073  -0.072   -0.045   -0.045
## 290      Im3 ~~     Im12  2.015 -0.024  -0.024   -0.094   -0.094
## 291     Im12 ~~     Im16  2.003  0.039   0.039    0.090    0.090
## 292      Im2 ~~    SAT_1  1.991 -0.025  -0.025   -0.087   -0.087
## 293     Im12 ~~    SAT_3  1.984  0.042   0.042    0.085    0.085
## 294     Im18 ~~   C_REP1  1.983  0.023   0.023    0.071    0.071
## 295     Im19 ~~   C_REP2  1.960  0.017   0.017    0.143    0.143
## 296     Im21 ~~    C_CR4  1.960  0.076   0.076    0.077    0.077
## 297     Im14 ~~     Im17  1.948  0.016   0.016    0.206    0.206
## 298      Im2 ~~   COM_A3  1.923  0.039   0.039    0.075    0.075
## 299      SAT =~     Im18  1.917 -0.073  -0.064   -0.046   -0.046
## 300     Im14 ~~   COM_A3  1.909  0.026   0.026    0.106    0.106
## 301     Im14 ~~      Im2  1.900  0.015   0.015    0.103    0.103
## 302     FOOD =~      Im1  1.888 -0.060  -0.049   -0.037   -0.037
## 303     Im12 ~~    SAT_1  1.877 -0.028  -0.028   -0.098   -0.098
## 304    C_CR1 ~~    C_CR3  1.851  0.543   0.543    0.451    0.451
## 305     Im10 ~~   COM_A4  1.834 -0.026  -0.026   -0.083   -0.083
## 306      Im7 ~~   COM_A1  1.820 -0.041  -0.041   -0.119   -0.119
## 307     Im11 ~~      Im7  1.810  0.040   0.040    0.112    0.112
## 308     Im11 ~~   COM_A3  1.799  0.058   0.058    0.068    0.068
## 309   COM_A3 ~~    SAT_2  1.794  0.042   0.042    0.078    0.078
## 310      SAT =~      Im2  1.787  0.065   0.056    0.044    0.044
## 311    BRAND =~      Im3  1.782  0.035   0.042    0.032    0.032
## 312     Im20 ~~    SAT_1  1.779 -0.036  -0.036   -0.086   -0.086
## 313   COM_A2 ~~    SAT_3  1.771  0.056   0.056    0.071    0.071
## 314   COM_A1 ~~   C_REP3  1.769  0.022   0.022    0.067    0.067
## 315   CHOICE =~    SAT_2  1.768 -0.041  -0.054   -0.054   -0.054
## 316   CHOICE =~    C_CR4  1.742  0.062   0.080    0.041    0.041
## 317    ATMOS =~    SAT_2  1.740  0.037   0.047    0.047    0.047
## 318     PROF =~      Im4  1.737 -0.065  -0.059   -0.044   -0.044
## 319     Im10 ~~    SAT_2  1.735 -0.016  -0.016   -0.083   -0.083
## 320   FRENCH =~      Im5  1.729  0.059   0.058    0.043    0.043
## 321     Im19 ~~     Im17  1.718  0.030   0.030    0.158    0.158
## 322   FRENCH =~    C_CR1  1.715 -0.080  -0.079   -0.041   -0.041
## 323     Im20 ~~   COM_A3  1.713 -0.057  -0.057   -0.075   -0.075
## 324      Im7 ~~   COM_A2  1.692 -0.042  -0.042   -0.119   -0.119
## 325      COI =~      Im1  1.689 -0.025  -0.042   -0.031   -0.031
## 326     Im12 ~~      Im6  1.663 -0.030  -0.030   -0.080   -0.080
## 327       RI =~     Im14  1.662  0.047   0.028    0.032    0.032
## 328       RI =~     Im10  1.662 -0.046  -0.027   -0.031   -0.031
## 329     Im13 ~~   COM_A4  1.659  0.046   0.046    0.080    0.080
## 330       RI =~      Im7  1.647 -0.094  -0.055   -0.046   -0.046
## 331     Im11 ~~      Im2  1.627  0.032   0.032    0.063    0.063
## 332      COI =~     Im22  1.622 -0.037  -0.061   -0.040   -0.040
## 333      Im3 ~~     Im14  1.617 -0.012  -0.012   -0.103   -0.103
## 334   C_REP1 ~~    C_CR3  1.612  0.036   0.036    0.069    0.069
## 335      Im5 ~~    SAT_2  1.610  0.034   0.034    0.068    0.068
## 336 PRODQUAL =~      Im4  1.608 -0.058  -0.041   -0.030   -0.030
## 337       RI =~     Im19  1.585 -0.099  -0.058   -0.052   -0.052
## 338     Im12 ~~    C_CR4  1.580  0.053   0.053    0.081    0.081
## 339      COI =~      Im4  1.558 -0.020  -0.032   -0.024   -0.024
## 340      SAT =~     Im17  1.554  0.057   0.049    0.040    0.040
## 341      Im7 ~~    SAT_3  1.540  0.038   0.038    0.107    0.107
## 342     Im12 ~~     Im17  1.539 -0.026  -0.026   -0.154   -0.154
## 343     Im17 ~~   COM_A1  1.518  0.033   0.033    0.124    0.124
## 344   FRENCH =~      Im2  1.509  0.038   0.037    0.029    0.029
## 345      Im1 ~~   COM_A4  1.504 -0.034  -0.034   -0.135   -0.135
## 346     Im10 ~~     Im18  1.499  0.018   0.018    0.071    0.071
## 347      Im4 ~~      Im2  1.495 -0.017  -0.017   -0.094   -0.094
## 348       RI =~     Im13  1.495  0.082   0.048    0.040    0.040
## 349   CHOICE =~     Im21  1.486  0.046   0.060    0.043    0.043
## 350      Im2 ~~     Im18  1.484 -0.026  -0.026   -0.063   -0.063
## 351   CHOICE  ~      SAT  1.479  0.210   0.140    0.140    0.140
## 352   C_REP3 ~~    C_CR4  1.479  0.027   0.027    0.064    0.064
## 353     Im11 ~~    SAT_1  1.457  0.033   0.033    0.070    0.070
## 354     PROF =~      Im5  1.424  0.081   0.074    0.055    0.055
## 355     DECO =~     Im13  1.423  0.045   0.055    0.046    0.046
## 356     Im12 ~~     Im13  1.421  0.088   0.088    0.252    0.252
## 357     Im18 ~~   COM_A2  1.416  0.041   0.041    0.064    0.064
## 358   COM_A1 ~~    SAT_2  1.415  0.034   0.034    0.067    0.067
## 359     FOOD =~      Im2  1.413  0.046   0.038    0.029    0.029
## 360     Im12 ~~   C_REP1  1.409 -0.018  -0.018   -0.071   -0.071
## 361    AFCOM  ~     DECO  1.398  0.054   0.059    0.059    0.059
## 362     DECO ~~      SAT  1.396 -0.146  -0.179   -0.179   -0.179
## 363     Im14 ~~     Im18  1.395 -0.016  -0.016   -0.088   -0.088
## 364     Im21 ~~    SAT_3  1.392  0.045   0.045    0.061    0.061
## 365      SAT =~   COM_A1  1.385  0.070   0.061    0.043    0.043
## 366      Im1 ~~   COM_A1  1.385  0.030   0.030    0.123    0.123
## 367     Im18 ~~      Im7  1.381 -0.029  -0.029   -0.103   -0.103
## 368   COM_A3 ~~    C_CR3  1.376  0.074   0.074    0.068    0.068
## 369    SAT_2 ~~    C_CR3  1.376  0.048   0.048    0.071    0.071
## 370     Im14 ~~    C_CR4  1.375  0.028   0.028    0.092    0.092
## 371     Im10 ~~     Im12  1.375  0.015   0.015    0.081    0.081
## 372      SAT =~      Im4  1.372 -0.039  -0.034   -0.025   -0.025
## 373    AFCOM =~     Im16  1.367 -0.047  -0.053   -0.044   -0.044
## 374      Im3 ~~     Im18  1.357 -0.022  -0.022   -0.066   -0.066
## 375     Im19 ~~     Im18  1.354 -0.031  -0.031   -0.068   -0.068
## 376     Im18 ~~   C_REP3  1.351 -0.015  -0.015   -0.058   -0.058
## 377    ATMOS =~     Im17  1.348 -0.052  -0.065   -0.053   -0.053
## 378    ATMOS =~     Im18  1.348  0.052   0.065    0.046    0.046
## 379      Im4 ~~     Im12  1.347  0.019   0.019    0.105    0.105
## 380   CHOICE =~   COM_A1  1.346  0.040   0.052    0.036    0.036
## 381      Im5 ~~     Im19  1.341 -0.034  -0.034   -0.064   -0.064
## 382     Im13 ~~    SAT_3  1.338 -0.037  -0.037   -0.066   -0.066
## 383      Im3 ~~     Im11  1.307  0.026   0.026    0.061    0.061
## 384    SAT_1 ~~    C_CR4  1.304  0.044   0.044    0.073    0.073
## 385    ATMOS =~   COM_A2  1.298 -0.055  -0.069   -0.043   -0.043
## 386     Im20 ~~   C_REP2  1.295  0.016   0.016    0.108    0.108
## 387    BRAND =~     Im16  1.284 -0.059  -0.071   -0.059   -0.059
## 388    SAT_1 ~~   C_REP3  1.284  0.013   0.013    0.067    0.067
## 389      Im6 ~~      Im7  1.281  0.435   0.435    1.612    1.612
## 390   FRENCH ~~    AFCOM  1.280 -0.077  -0.085   -0.085   -0.085
## 391       RI =~   COM_A3  1.276  0.094   0.055    0.034    0.034
## 392 PRODQUAL =~     Im17  1.271  0.103   0.072    0.058    0.058
## 393 PRODQUAL =~     Im18  1.271 -0.102  -0.072   -0.051   -0.051
## 394     Im14 ~~     Im21  1.262  0.018   0.018    0.084    0.084
## 395     Im22 ~~    C_CR1  1.256 -0.058  -0.058   -0.075   -0.075
## 396     Im12 ~~   COM_A4  1.239 -0.037  -0.037   -0.072   -0.072
## 397       RI =~   COM_A4  1.230  0.093   0.055    0.032    0.032
## 398     Im20 ~~   C_REP3  1.225 -0.018  -0.018   -0.059   -0.059
## 399      Im3 ~~     Im10  1.223  0.011   0.011    0.070    0.070
## 400 PRODQUAL =~   COM_A2  1.213 -0.078  -0.055   -0.035   -0.035
## 401   FRENCH =~    SAT_3  1.209  0.051   0.050    0.044    0.044
## 402     Im10 ~~    C_CR4  1.207 -0.027  -0.027   -0.067   -0.067
## 403      Im4 ~~   COM_A4  1.202 -0.027  -0.027   -0.089   -0.089
## 404 PRODQUAL =~     Im20  1.186  0.083   0.058    0.039    0.039
## 405     PROF ~~    AFCOM  1.182  0.034   0.040    0.040    0.040
## 406   CHOICE =~    SAT_1  1.178  0.035   0.046    0.045    0.045
## 407      COI =~     Im20  1.152 -0.031  -0.051   -0.034   -0.034
## 408 PRODQUAL =~     Im22  1.149 -0.083  -0.058   -0.038   -0.038
## 409     Im10 ~~   C_REP3  1.147 -0.007  -0.007   -0.060   -0.060
## 410    SAT_1 ~~    C_CR3  1.144 -0.042  -0.042   -0.070   -0.070
## 411      COI =~    SAT_2  1.136  0.020   0.034    0.034    0.034
## 412     Im16 ~~      Im7  1.135 -0.030  -0.030   -0.098   -0.098
## 413 PRODQUAL =~     Im19  1.134  0.088   0.062    0.055    0.055
## 414      Im1 ~~   COM_A3  1.105 -0.029  -0.029   -0.113   -0.113
## 415     Im16 ~~    C_CR1  1.098  0.052   0.052    0.064    0.064
## 416      Im4 ~~      Im7  1.087 -0.018  -0.018   -0.137   -0.137
## 417     Im17 ~~   COM_A3  1.087  0.031   0.031    0.108    0.108
## 418     PROF =~      Im7  1.079 -0.065  -0.059   -0.049   -0.049
## 419    BRAND =~     Im11  1.044 -0.046  -0.055   -0.048   -0.048
## 420     PROF =~   COM_A1  1.028  0.055   0.050    0.035    0.035
## 421      Im1 ~~   COM_A2  1.000  0.027   0.027    0.108    0.108
## 422      Im6 ~~    SAT_1  0.995  0.022   0.022    0.062    0.062
## 423     Im13 ~~    C_CR3  0.995 -0.046  -0.046   -0.063   -0.063
## 424     Im14 ~~     Im12  0.989 -0.013  -0.013   -0.089   -0.089
## 425   COM_A4 ~~    C_CR3  0.982 -0.063  -0.063   -0.059   -0.059
## 426    SAT_3 ~~   C_REP3  0.980  0.016   0.016    0.049    0.049
## 427      Im1 ~~     Im18  0.980  0.021   0.021    0.104    0.104
## 428   CHOICE =~     Im16  0.965  0.048   0.063    0.052    0.052
## 429   CHOICE =~     Im19  0.965 -0.050  -0.065   -0.058   -0.058
## 430    ATMOS =~      Im2  0.957 -0.032  -0.040   -0.031   -0.031
## 431     Im16 ~~   COM_A3  0.956  0.040   0.040    0.054    0.054
## 432     Im20 ~~     Im18  0.950  0.032   0.032    0.054    0.054
## 433     Im17 ~~   COM_A4  0.902 -0.028  -0.028   -0.101   -0.101
## 434      Im5 ~~      Im2  0.897 -0.023  -0.023   -0.047   -0.047
## 435     Im13 ~~     Im18  0.892 -0.025  -0.025   -0.056   -0.056
## 436    BRAND =~    SAT_3  0.890 -0.037  -0.045   -0.040   -0.040
## 437    ATMOS =~      Im3  0.886  0.024   0.029    0.022    0.022
## 438    ATMOS =~    C_CR3  0.882 -0.050  -0.063   -0.031   -0.031
## 439   CHOICE ~~      SAT  0.882 -0.110  -0.128   -0.128   -0.128
## 440      Im1 ~~      Im2  0.880  1.034   1.034    6.695    6.695
## 441      SAT =~     Im21  0.870  0.051   0.044    0.032    0.032
## 442     Im11 ~~   COM_A2  0.868  0.038   0.038    0.048    0.048
## 443     FOOD =~     Im20  0.862 -0.054  -0.044   -0.029   -0.029
## 444     Im17 ~~   C_REP3  0.860  0.010   0.010    0.090    0.090
## 445      SAT =~      Im1  0.859 -0.049  -0.043   -0.032   -0.032
## 446    ATMOS ~~      SAT  0.859  0.034   0.041    0.041    0.041
## 447      Im7 ~~   COM_A4  0.857  0.031   0.031    0.087    0.087
## 448     Im11 ~~    C_CR4  0.857  0.051   0.051    0.048    0.048
## 449     DECO =~   C_REP2  0.849 -0.014  -0.017   -0.027   -0.027
## 450      Im6 ~~    C_CR4  0.847 -0.041  -0.041   -0.051   -0.051
## 451      Im3 ~~    SAT_1  0.845  0.015   0.015    0.061    0.061
## 452     DECO =~    SAT_2  0.832  0.026   0.033    0.033    0.033
## 453     Im19 ~~    SAT_3  0.832 -0.029  -0.029   -0.052   -0.052
## 454     Im16 ~~   COM_A4  0.828 -0.037  -0.037   -0.052   -0.052
## 455      Im6 ~~   COM_A1  0.825  0.029   0.029    0.048    0.048
## 456      Im6 ~~   C_REP2  0.824  0.010   0.010    0.081    0.081
## 457    BRAND =~      Im1  0.818 -0.039  -0.047   -0.035   -0.035
## 458      Im4 ~~    C_CR3  0.817  0.029   0.029    0.074    0.074
## 459      Im4 ~~   COM_A2  0.807 -0.021  -0.021   -0.071   -0.071
## 460      COI =~    SAT_3  0.791 -0.024  -0.040   -0.035   -0.035
## 461      Im7 ~~    C_CR4  0.785  0.038   0.038    0.082    0.082
## 462    SAT_2 ~~   C_REP3  0.783  0.010   0.010    0.048    0.048
## 463    BRAND =~   COM_A4  0.778 -0.037  -0.045   -0.026   -0.026
## 464     Im16 ~~    SAT_2  0.778  0.024   0.024    0.052    0.052
## 465     Im20 ~~     Im12  0.776  0.026   0.026    0.058    0.058
## 466     PROF =~     Im18  0.772 -0.078  -0.071   -0.051   -0.051
## 467     PROF =~     Im17  0.772  0.079   0.072    0.058    0.058
## 468     FOOD =~    SAT_3  0.770  0.050   0.040    0.036    0.036
## 469      COI =~      Im5  0.767  0.022   0.037    0.028    0.028
## 470     Im17 ~~   C_REP2  0.767  0.009   0.009    0.155    0.155
## 471      Im7 ~~    C_CR1  0.757 -0.035  -0.035   -0.087   -0.087
## 472   FRENCH =~   COM_A1  0.751 -0.042  -0.042   -0.029   -0.029
## 473   CHOICE =~   C_REP2  0.751 -0.012  -0.016   -0.026   -0.026
## 474     Im14 ~~    SAT_1  0.748 -0.010  -0.010   -0.075   -0.075
## 475     Im21 ~~     Im11  0.737 -0.032  -0.032   -0.043   -0.043
## 476      Im3 ~~     Im19  0.732  0.016   0.016    0.055    0.055
## 477     PROF =~     Im11  0.726  0.054   0.049    0.043    0.043
## 478    BRAND =~      Im2  0.725  0.033   0.039    0.031    0.031
## 479     Im12 ~~   COM_A3  0.724 -0.028  -0.028   -0.054   -0.054
## 480      Im1 ~~   C_REP2  0.720  0.008   0.008    0.154    0.154
## 481     Im14 ~~     Im13  0.716  0.012   0.012    0.072    0.072
## 482     Im20 ~~      Im2  0.715 -0.021  -0.021   -0.047   -0.047
## 483      Im2 ~~   C_REP3  0.715  0.009   0.009    0.043    0.043
## 484    BRAND =~   COM_A2  0.713 -0.034  -0.041   -0.026   -0.026
## 485      Im5 ~~    C_CR3  0.707 -0.045  -0.045   -0.045   -0.045
## 486      Im7 ~~   C_REP3  0.706  0.010   0.010    0.071    0.071
## 487      Im5 ~~    C_CR4  0.704  0.044   0.044    0.044    0.044
## 488   COM_A3 ~~    SAT_3  0.702 -0.037  -0.037   -0.044   -0.044
## 489     Im21 ~~     Im17  0.698  0.022   0.022    0.085    0.085
## 490      Im3 ~~    C_CR4  0.696 -0.027  -0.027   -0.049   -0.049
## 491     Im12 ~~   COM_A2  0.654  0.026   0.026    0.052    0.052
## 492     FOOD =~   COM_A2  0.653 -0.047  -0.038   -0.024   -0.024
## 493   COM_A4 ~~   C_REP3  0.652 -0.014  -0.014   -0.043   -0.043
## 494 PRODQUAL =~    SAT_1  0.651 -0.042  -0.029   -0.029   -0.029
## 495     Im21 ~~   C_REP1  0.650 -0.015  -0.015   -0.041   -0.041
## 496      Im4 ~~      Im5  0.638  0.028   0.028    0.099    0.099
## 497    ATMOS =~      Im1  0.638  0.029   0.036    0.027    0.027
## 498    BRAND =~     Im14  0.638  0.015   0.018    0.021    0.021
## 499    BRAND =~     Im10  0.638 -0.015  -0.018   -0.020   -0.020
## 500   FRENCH =~     Im13  0.638 -0.033  -0.033   -0.027   -0.027
## 501    AFCOM =~   C_REP2  0.636 -0.012  -0.014   -0.022   -0.022
## 502      SAT  ~ PRODQUAL  0.629  0.055   0.045    0.045    0.045
## 503 PRODQUAL =~   COM_A3  0.623  0.058   0.041    0.025    0.025
## 504      SAT =~     Im14  0.623  0.020   0.018    0.021    0.021
## 505 PRODQUAL  ~      SAT  0.621 -0.038  -0.047   -0.047   -0.047
## 506    ATMOS =~     Im19  0.620 -0.034  -0.043   -0.038   -0.038
## 507      Im4 ~~     Im10  0.613 -0.008  -0.008   -0.067   -0.067
## 508      Im2 ~~   COM_A4  0.612  0.022   0.022    0.043    0.043
## 509       RI =~      Im1  0.609 -0.046  -0.027   -0.020   -0.020
## 510     Im10 ~~      Im2  0.608 -0.009  -0.009   -0.045   -0.045
## 511     Im10 ~~   COM_A3  0.603 -0.015  -0.015   -0.046   -0.046
## 512    ATMOS =~   COM_A3  0.600  0.039   0.048    0.030    0.030
## 513     Im12 ~~    C_CR1  0.600 -0.031  -0.031   -0.054   -0.054
## 514     FOOD ~~      SAT  0.598  0.017   0.032    0.032    0.032
## 515   COM_A2 ~~    C_CR4  0.598 -0.046  -0.046   -0.044   -0.044
## 516     Im22 ~~     Im13  0.597 -0.024  -0.024   -0.051   -0.051
## 517     Im10 ~~   COM_A1  0.593 -0.014  -0.014   -0.045   -0.045
## 518       RI =~      Im4  0.589 -0.034  -0.020   -0.015   -0.015
## 519     Im21 ~~     Im12  0.585  0.022   0.022    0.047    0.047
## 520      Im7 ~~   C_REP1  0.583  0.011   0.011    0.065    0.065
## 521    SAT_3 ~~    C_CR1  0.582  0.041   0.041    0.044    0.044
## 522      Im4 ~~    C_CR4  0.581  0.024   0.024    0.061    0.061
## 523      Im7 ~~   COM_A3  0.566  0.025   0.025    0.068    0.068
## 524     Im20 ~~      Im7  0.551  0.022   0.022    0.070    0.070
## 525     Im14 ~~     Im22  0.549 -0.012  -0.012   -0.063   -0.063
## 526     Im10 ~~     Im21  0.543 -0.012  -0.012   -0.043   -0.043
## 527      Im4 ~~     Im16  0.541  0.015   0.015    0.059    0.059
## 528     PROF =~     Im22  0.532  0.048   0.043    0.028    0.028
## 529      COI =~      Im3  0.531  0.011   0.019    0.014    0.014
## 530   FRENCH =~     Im21  0.520 -0.034  -0.034   -0.025   -0.025
## 531     Im22 ~~      Im6  0.520  0.022   0.022    0.043    0.043
## 532      Im6 ~~   COM_A3  0.519 -0.025  -0.025   -0.039   -0.039
## 533      Im7 ~~    SAT_1  0.513  0.015   0.015    0.074    0.074
## 534     Im22 ~~     Im16  0.512  0.026   0.026    0.043    0.043
## 535 PRODQUAL =~   C_REP2  0.505  0.020   0.014    0.022    0.022
## 536     Im14 ~~   COM_A4  0.504  0.013   0.013    0.056    0.056
## 537     Im11 ~~     Im18  0.501  0.023   0.023    0.035    0.035
## 538      SAT =~    C_CR3  0.500 -0.053  -0.046   -0.022   -0.022
## 539     Im17 ~~    SAT_3  0.500 -0.019  -0.019   -0.070   -0.070
## 540      Im5 ~~     Im11  0.498  0.026   0.026    0.033    0.033
## 541     Im20 ~~    C_CR3  0.491 -0.040  -0.040   -0.042   -0.042
## 542      Im3 ~~      Im7  0.490 -0.012  -0.012   -0.067   -0.067
## 543     Im10 ~~     Im20  0.488  0.012   0.012    0.043    0.043
## 544   CHOICE =~    C_CR1  0.484 -0.031  -0.041   -0.021   -0.021
## 545     Im14 ~~     Im20  0.479 -0.012  -0.012   -0.055   -0.055
## 546     Im12 ~~      Im2  0.478 -0.013  -0.013   -0.043   -0.043
## 547      Im5 ~~     Im10  0.477 -0.011  -0.011   -0.038   -0.038
## 548     Im21 ~~      Im7  0.471 -0.020  -0.020   -0.061   -0.061
## 549      Im1 ~~    C_CR1  0.468 -0.023  -0.023   -0.082   -0.082
## 550     Im10 ~~    SAT_1  0.467  0.008   0.008    0.047    0.047
## 551      Im2 ~~   COM_A1  0.467 -0.018  -0.018   -0.036   -0.036
## 552 PRODQUAL =~     Im14  0.462  0.027   0.019    0.022    0.022
## 553 PRODQUAL =~     Im10  0.462 -0.026  -0.018   -0.021   -0.021
## 554      Im5 ~~     Im21  0.461 -0.025  -0.025   -0.034   -0.034
## 555     Im12 ~~    SAT_2  0.459 -0.014  -0.014   -0.045   -0.045
## 556      COI =~     Im16  0.453 -0.018  -0.030   -0.025   -0.025
## 557 PRODQUAL =~   C_REP1  0.445  0.022   0.016    0.021    0.021
## 558    BRAND =~     Im19  0.445  0.034   0.040    0.036    0.036
## 559    C_CR1 ~~    C_CR4  0.442 -0.240  -0.240   -0.200   -0.200
## 560     PROF =~      Im3  0.441  0.032   0.029    0.022    0.022
## 561   COM_A1 ~~   C_REP1  0.435 -0.013  -0.013   -0.034   -0.034
## 562    AFCOM =~     Im13  0.435 -0.023  -0.026   -0.021   -0.021
## 563    AFCOM =~    C_CR3  0.434  0.038   0.042    0.020    0.020
## 564     Im19 ~~    SAT_2  0.434  0.015   0.015    0.043    0.043
## 565   CHOICE =~      Im4  0.434 -0.015  -0.019   -0.014   -0.014
## 566     Im12 ~~   C_REP3  0.433 -0.008  -0.008   -0.039   -0.039
## 567     PROF =~      Im6  0.430  0.035   0.032    0.027    0.027
## 568      COI =~   COM_A3  0.429  0.020   0.032    0.020    0.020
## 569   CHOICE =~     Im11  0.426 -0.025  -0.032   -0.028   -0.028
## 570      Im1 ~~     Im16  0.420 -0.016  -0.016   -0.072   -0.072
## 571   CHOICE =~      Im3  0.410 -0.014  -0.019   -0.014   -0.014
## 572    SAT_1 ~~   C_REP2  0.407 -0.006  -0.006   -0.066   -0.066
## 573      Im6 ~~    SAT_3  0.403 -0.020  -0.020   -0.033   -0.033
## 574     Im13 ~~      Im6  0.401  0.016   0.016    0.038    0.038
## 575    AFCOM =~      Im4  0.399 -0.015  -0.016   -0.012   -0.012
## 576       RI =~   COM_A2  0.395 -0.050  -0.029   -0.018   -0.018
## 577    C_CR3 ~~    C_CR4  0.394 -0.226  -0.226   -0.165   -0.165
## 578     Im20 ~~   C_REP1  0.388 -0.012  -0.012   -0.033   -0.033
## 579     Im11 ~~    C_CR3  0.385  0.035   0.035    0.033    0.033
## 580   FRENCH =~    SAT_2  0.383  0.021   0.020    0.020    0.020
## 581     Im12 ~~   C_REP2  0.378  0.007   0.007    0.065    0.065
## 582     Im10 ~~    SAT_3  0.377  0.011   0.011    0.035    0.035
## 583    ATMOS  ~      SAT  0.371 -0.052  -0.036   -0.036   -0.036
## 584     Im13 ~~     Im19  0.371  0.016   0.016    0.040    0.040
## 585     DECO =~    SAT_3  0.370 -0.023  -0.028   -0.025   -0.025
## 586      Im2 ~~      Im7  0.369  0.012   0.012    0.053    0.053
## 587    SAT_2 ~~   C_REP2  0.368  0.006   0.006    0.058    0.058
## 588     Im14 ~~   C_REP2  0.367 -0.004  -0.004   -0.078   -0.078
## 589    AFCOM =~      Im6  0.367  0.022   0.025    0.021    0.021
## 590   COM_A1 ~~    C_CR4  0.359 -0.034  -0.034   -0.033   -0.033
## 591      Im1 ~~    SAT_3  0.354  0.015   0.015    0.061    0.061
## 592     FOOD =~      Im3  0.352 -0.021  -0.017   -0.013   -0.013
## 593      Im6 ~~   COM_A2  0.352  0.020   0.020    0.033    0.033
## 594    ATMOS =~     Im16  0.351 -0.027  -0.033   -0.028   -0.028
## 595      Im5 ~~     Im22  0.351  0.022   0.022    0.033    0.033
## 596 PRODQUAL =~   COM_A1  0.350  0.040   0.028    0.020    0.020
## 597   C_REP2 ~~    C_CR3  0.348  0.012   0.012    0.056    0.056
## 598     Im17 ~~   COM_A2  0.346 -0.017  -0.017   -0.061   -0.061
## 599      Im5 ~~     Im17  0.344  0.015   0.015    0.056    0.056
## 600     Im11 ~~   C_REP3  0.343  0.009   0.009    0.028    0.028
## 601   COM_A3 ~~    SAT_1  0.342  0.018   0.018    0.037    0.037
## 602   CHOICE =~   COM_A4  0.338 -0.022  -0.029   -0.017   -0.017
## 603      Im3 ~~   COM_A2  0.336 -0.014  -0.014   -0.034   -0.034
## 604      Im3 ~~   COM_A1  0.336 -0.013  -0.013   -0.033   -0.033
## 605     Im17 ~~    C_CR1  0.333 -0.021  -0.021   -0.067   -0.067
## 606   FRENCH =~      Im3  0.330 -0.016  -0.016   -0.012   -0.012
## 607      Im6 ~~    C_CR1  0.326  0.024   0.024    0.034    0.034
## 608     Im11 ~~   COM_A1  0.321 -0.022  -0.022   -0.028   -0.028
## 609   COM_A4 ~~    SAT_2  0.316  0.018   0.018    0.034    0.034
## 610    SAT_2 ~~    C_CR1  0.314 -0.021  -0.021   -0.036   -0.036
## 611   FRENCH =~   COM_A4  0.312  0.031   0.030    0.018    0.018
## 612      Im3 ~~     Im13  0.310  0.010   0.010    0.035    0.035
## 613     Im19 ~~    C_CR3  0.309  0.025   0.025    0.035    0.035
## 614   CHOICE =~    C_CR3  0.303 -0.026  -0.035   -0.017   -0.017
## 615      Im3 ~~    SAT_2  0.303 -0.009  -0.009   -0.034   -0.034
## 616     Im13 ~~      Im7  0.303 -0.014  -0.014   -0.055   -0.055
## 617      Im5 ~~   C_REP2  0.302 -0.007  -0.007   -0.046   -0.046
## 618     Im17 ~~      Im7  0.301 -0.012  -0.012   -0.099   -0.099
## 619     Im18 ~~    SAT_1  0.296 -0.012  -0.012   -0.033   -0.033
## 620     Im19 ~~    C_CR1  0.292  0.023   0.023    0.036    0.036
## 621     Im21 ~~     Im13  0.288 -0.017  -0.017   -0.032   -0.032
## 622    AFCOM =~      Im7  0.287 -0.022  -0.024   -0.020   -0.020
## 623    AFCOM =~     Im14  0.284  0.010   0.011    0.013    0.013
## 624   COM_A1 ~~    C_CR1  0.282 -0.028  -0.028   -0.031   -0.031
## 625      Im4 ~~     Im14  0.279  0.005   0.005    0.058    0.058
## 626      Im5 ~~     Im20  0.279  0.020   0.020    0.028    0.028
## 627      COI =~   C_REP3  0.279 -0.006  -0.010   -0.017   -0.017
## 628     Im17 ~~    C_CR3  0.278  0.021   0.021    0.057    0.057
## 629     Im21 ~~   COM_A4  0.277 -0.023  -0.023   -0.029   -0.029
## 630   CHOICE =~     Im17  0.275  0.022   0.028    0.023    0.023
## 631   CHOICE =~     Im18  0.275 -0.021  -0.028   -0.020   -0.020
## 632     Im22 ~~   COM_A2  0.272  0.021   0.021    0.032    0.032
## 633      Im2 ~~    C_CR4  0.271 -0.019  -0.019   -0.029   -0.029
## 634     Im21 ~~     Im16  0.271 -0.019  -0.019   -0.028   -0.028
## 635      Im4 ~~   C_REP3  0.271 -0.005  -0.005   -0.038   -0.038
## 636      COI =~      Im6  0.265 -0.011  -0.018   -0.015   -0.015
## 637      Im7 ~~    SAT_2  0.262 -0.011  -0.011   -0.049   -0.049
## 638   CHOICE =~      Im6  0.256 -0.014  -0.019   -0.016   -0.016
## 639     Im17 ~~    SAT_2  0.247  0.009   0.009    0.054    0.054
## 640     Im20 ~~     Im19  0.247  0.016   0.016    0.031    0.031
## 641      COI =~     Im12  0.243  0.011   0.018    0.016    0.016
## 642     DECO =~    SAT_1  0.242 -0.015  -0.018   -0.018   -0.018
## 643      SAT =~      Im6  0.242  0.022   0.019    0.016    0.016
## 644     Im16 ~~   C_REP1  0.239  0.009   0.009    0.025    0.025
## 645     Im18 ~~   C_REP2  0.237 -0.006  -0.006   -0.043   -0.043
## 646     DECO =~     Im11  0.231  0.019   0.024    0.021    0.021
## 647    SAT_3 ~~   C_REP1  0.230 -0.009  -0.009   -0.024   -0.024
## 648     Im10 ~~     Im19  0.230 -0.007  -0.007   -0.032   -0.032
## 649     DECO =~   COM_A4  0.229  0.019   0.024    0.014    0.014
## 650      Im4 ~~    SAT_1  0.225 -0.007  -0.007   -0.043   -0.043
## 651     Im14 ~~   C_REP1  0.224  0.004   0.004    0.034    0.034
## 652     PROF =~   C_REP2  0.222 -0.011  -0.010   -0.016   -0.016
## 653     Im20 ~~    SAT_3  0.218  0.018   0.018    0.025    0.025
## 654    SAT_3 ~~    C_CR4  0.215  0.026   0.026    0.025    0.025
## 655     Im16 ~~     Im18  0.213 -0.014  -0.014   -0.025   -0.025
## 656     Im11 ~~    SAT_2  0.212 -0.013  -0.013   -0.025   -0.025
## 657     FOOD =~   COM_A4  0.212 -0.028  -0.023   -0.013   -0.013
## 658     PROF =~    SAT_3  0.209 -0.033  -0.030   -0.026   -0.026
## 659     Im21 ~~    SAT_1  0.208  0.012   0.012    0.028    0.028
## 660     Im21 ~~    SAT_2  0.207 -0.012  -0.012   -0.026   -0.026
## 661     Im22 ~~     Im17  0.206  0.012   0.012    0.053    0.053
## 662      Im5 ~~    SAT_1  0.205 -0.012  -0.012   -0.026   -0.026
## 663    AFCOM =~    SAT_3  0.204  0.020   0.023    0.020    0.020
## 664      Im3 ~~   C_REP2  0.199 -0.004  -0.004   -0.043   -0.043
## 665      Im4 ~~   C_REP2  0.198  0.004   0.004    0.058    0.058
## 666      SAT =~   COM_A4  0.197  0.030   0.026    0.015    0.015
## 667 PRODQUAL =~    C_CR3  0.195 -0.041  -0.029   -0.014   -0.014
## 668     Im12 ~~    C_CR3  0.194  0.019   0.019    0.029    0.029
## 669      SAT =~      Im7  0.191  0.021   0.018    0.015    0.015
## 670     Im11 ~~    C_CR1  0.188 -0.023  -0.023   -0.024   -0.024
## 671     Im13 ~~   COM_A1  0.187  0.014   0.014    0.025    0.025
## 672      Im6 ~~   C_REP1  0.185 -0.007  -0.007   -0.022   -0.022
## 673       RI =~     Im20  0.180 -0.036  -0.021   -0.014   -0.014
## 674      Im4 ~~   COM_A1  0.174  0.009   0.009    0.032    0.032
## 675    BRAND =~     Im21  0.174 -0.018  -0.022   -0.016   -0.016
## 676    AFCOM =~     Im18  0.174 -0.015  -0.017   -0.012   -0.012
## 677      Im5 ~~   COM_A3  0.173 -0.017  -0.017   -0.021   -0.021
## 678    AFCOM =~    SAT_1  0.171 -0.015  -0.016   -0.016   -0.016
## 679     Im21 ~~      Im2  0.169  0.010   0.010    0.022    0.022
## 680     Im21 ~~     Im19  0.169 -0.013  -0.013   -0.024   -0.024
## 681     Im16 ~~   C_REP2  0.168 -0.006  -0.006   -0.038   -0.038
## 682   COM_A4 ~~    C_CR1  0.167  0.024   0.024    0.025    0.025
## 683   COM_A2 ~~   C_REP3  0.164 -0.007  -0.007   -0.021   -0.021
## 684     Im20 ~~     Im11  0.164  0.016   0.016    0.021    0.021
## 685     Im22 ~~    C_CR3  0.164  0.023   0.023    0.026    0.026
## 686    ATMOS =~    SAT_1  0.163  0.011   0.014    0.014    0.014
## 687       RI =~     Im18  0.162 -0.027  -0.016   -0.011   -0.011
## 688       RI =~     Im17  0.162  0.027   0.016    0.013    0.013
## 689     DECO ~~    AFCOM  0.161  0.017   0.015    0.015    0.015
## 690      Im1 ~~    C_CR3  0.161 -0.015  -0.015   -0.045   -0.045
## 691     Im16 ~~   COM_A1  0.154 -0.015  -0.015   -0.021   -0.021
## 692     Im12 ~~     Im19  0.151  0.009   0.009    0.027    0.027
## 693     Im10 ~~     Im22  0.151  0.007   0.007    0.026    0.026
## 694     Im22 ~~   COM_A4  0.151  0.017   0.017    0.024    0.024
## 695     Im14 ~~     Im11  0.150  0.006   0.006    0.027    0.027
## 696      Im2 ~~      Im6  0.146 -0.008  -0.008   -0.020   -0.020
## 697     Im14 ~~      Im1  0.145 -0.004  -0.004   -0.058   -0.058
## 698      Im3 ~~   C_REP1  0.142  0.004   0.004    0.021    0.021
## 699       RI =~    C_CR3  0.140  0.041   0.024    0.012    0.012
## 700     Im21 ~~   C_REP2  0.139 -0.005  -0.005   -0.033   -0.033
## 701      SAT =~     Im10  0.138 -0.010  -0.008   -0.010   -0.010
## 702     FOOD =~     Im19  0.138 -0.024  -0.020   -0.017   -0.017
## 703    BRAND =~    SAT_1  0.137 -0.011  -0.013   -0.013   -0.013
## 704      Im4 ~~     Im13  0.137 -0.007  -0.007   -0.032   -0.032
## 705     FOOD =~   COM_A1  0.137 -0.021  -0.017   -0.012   -0.012
## 706     PROF =~    C_CR3  0.136 -0.027  -0.024   -0.012   -0.012
## 707      Im4 ~~     Im20  0.136  0.008   0.008    0.030    0.030
## 708     Im13 ~~    C_CR1  0.134 -0.016  -0.016   -0.024   -0.024
## 709     Im17 ~~      Im6  0.133  0.008   0.008    0.037    0.037
## 710      Im3 ~~    C_CR3  0.132 -0.012  -0.012   -0.022   -0.022
## 711     Im19 ~~      Im6  0.132 -0.009  -0.009   -0.021   -0.021
## 712      Im2 ~~    C_CR3  0.128  0.013   0.013    0.020    0.020
## 713     Im12 ~~     Im18  0.126 -0.009  -0.009   -0.022   -0.022
## 714     FOOD =~      Im4  0.124 -0.013  -0.010   -0.008   -0.008
## 715       RI =~      Im2  0.123  0.018   0.011    0.008    0.008
## 716     Im17 ~~    SAT_1  0.123  0.006   0.006    0.041    0.041
## 717     Im19 ~~    C_CR4  0.122  0.016   0.016    0.021    0.021
## 718     DECO  ~      SAT  0.119 -0.057  -0.040   -0.040   -0.040
## 719      Im1 ~~      Im7  0.119 -0.007  -0.007   -0.063   -0.063
## 720     Im19 ~~      Im7  0.119  0.009   0.009    0.036    0.036
## 721   FRENCH =~     Im17  0.118 -0.014  -0.014   -0.011   -0.011
## 722   FRENCH =~     Im18  0.118  0.014   0.014    0.010    0.010
## 723      Im4 ~~     Im19  0.113 -0.006  -0.006   -0.030   -0.030
## 724     Im16 ~~    SAT_3  0.111  0.012   0.012    0.018    0.018
## 725      SAT =~   C_REP3  0.109  0.007   0.006    0.011    0.011
## 726     FOOD =~     Im21  0.109  0.018   0.015    0.011    0.011
## 727   COM_A3 ~~    C_CR4  0.109 -0.020  -0.020   -0.019   -0.019
## 728     Im18 ~~    C_CR3  0.109 -0.016  -0.016   -0.018   -0.018
## 729    AFCOM =~     Im19  0.108  0.012   0.013    0.012    0.012
## 730    AFCOM =~      Im1  0.108 -0.009  -0.010   -0.008   -0.008
## 731      COI =~   COM_A1  0.107  0.009   0.015    0.010    0.010
## 732      Im3 ~~      Im6  0.106  0.006   0.006    0.019    0.019
## 733     Im21 ~~      Im1  0.105  0.008   0.008    0.034    0.034
## 734     Im21 ~~   COM_A1  0.101  0.012   0.012    0.017    0.017
## 735      COI =~      Im7  0.100 -0.008  -0.013   -0.011   -0.011
## 736     Im17 ~~    C_CR4  0.098  0.012   0.012    0.033    0.033
## 737   CHOICE =~    SAT_3  0.098  0.012   0.016    0.014    0.014
## 738      COI =~     Im14  0.098 -0.004  -0.006   -0.007   -0.007
## 739      COI =~     Im10  0.098  0.004   0.006    0.007    0.007
## 740     FOOD =~     Im22  0.098  0.018   0.015    0.010    0.010
## 741      Im6 ~~   C_REP3  0.097 -0.004  -0.004   -0.016   -0.016
## 742      SAT =~      Im3  0.097  0.010   0.009    0.007    0.007
## 743     Im10 ~~   C_REP2  0.097 -0.002  -0.002   -0.031   -0.031
## 744     Im12 ~~   COM_A1  0.096  0.009   0.009    0.019    0.019
## 745     Im21 ~~    C_CR1  0.096  0.016   0.016    0.018    0.018
## 746       RI =~      Im6  0.094  0.019   0.011    0.010    0.010
## 747   C_REP3 ~~    C_CR1  0.093  0.007   0.007    0.017    0.017
## 748    ATMOS =~      Im6  0.092 -0.010  -0.013   -0.011   -0.011
## 749    ATMOS =~      Im7  0.092  0.012   0.015    0.012    0.012
## 750    AFCOM =~     Im10  0.092 -0.006  -0.006   -0.007   -0.007
## 751     DECO  ~    AFCOM  0.090  0.015   0.013    0.013    0.013
## 752    ATMOS =~    SAT_3  0.086 -0.011  -0.014   -0.012   -0.012
## 753      Im5 ~~   COM_A4  0.085 -0.012  -0.012   -0.015   -0.015
## 754      Im5 ~~     Im18  0.084  0.009   0.009    0.014    0.014
## 755    AFCOM =~     Im17  0.084  0.009   0.010    0.008    0.008
## 756     Im10 ~~   C_REP1  0.082  0.002   0.002    0.016    0.016
## 757      Im4 ~~     Im21  0.080  0.006   0.006    0.022    0.022
## 758   FRENCH =~    C_CR3  0.077 -0.018  -0.018   -0.009   -0.009
## 759     DECO =~     Im21  0.077 -0.011  -0.014   -0.010   -0.010
## 760      Im6 ~~    SAT_2  0.076 -0.006  -0.006   -0.016   -0.016
## 761     Im22 ~~   COM_A3  0.075  0.012   0.012    0.017    0.017
## 762     FOOD =~    C_CR3  0.073 -0.021  -0.017   -0.008   -0.008
## 763     DECO =~     Im19  0.072  0.016   0.020    0.018    0.018
## 764     DECO =~     Im16  0.072 -0.016  -0.019   -0.016   -0.016
## 765      Im3 ~~   C_REP3  0.072  0.002   0.002    0.015    0.015
## 766   FRENCH =~     Im12  0.071 -0.011  -0.010   -0.009   -0.009
## 767      Im4 ~~   C_REP1  0.070 -0.003  -0.003   -0.020   -0.020
## 768      Im7 ~~    C_CR3  0.068 -0.011  -0.011   -0.025   -0.025
## 769     Im11 ~~     Im19  0.067 -0.008  -0.008   -0.014   -0.014
## 770     Im14 ~~    SAT_3  0.066 -0.004  -0.004   -0.019   -0.019
## 771      SAT =~     Im22  0.065 -0.015  -0.013   -0.008   -0.008
## 772      Im5 ~~    C_CR1  0.065  0.013   0.013    0.014    0.014
## 773      Im5 ~~   COM_A1  0.065 -0.010  -0.010   -0.013   -0.013
## 774     Im10 ~~    C_CR3  0.065 -0.006  -0.006   -0.016   -0.016
## 775     PROF =~   COM_A4  0.063 -0.015  -0.014   -0.008   -0.008
## 776      Im5 ~~    SAT_3  0.061 -0.009  -0.009   -0.012   -0.012
## 777     Im21 ~~   COM_A2  0.060  0.010   0.010    0.013    0.013
## 778     Im16 ~~      Im6  0.060 -0.007  -0.007   -0.013   -0.013
## 779     Im20 ~~     Im16  0.059  0.009   0.009    0.014    0.014
## 780     PROF =~     Im21  0.059  0.015   0.013    0.010    0.010
## 781      Im2 ~~     Im19  0.058 -0.005  -0.005   -0.014   -0.014
## 782      Im5 ~~     Im12  0.058  0.007   0.007    0.014    0.014
## 783    ATMOS =~     Im14  0.057  0.004   0.005    0.006    0.006
## 784      Im1 ~~      Im6  0.057 -0.005  -0.005   -0.025   -0.025
## 785    ATMOS =~     Im10  0.057 -0.004  -0.005   -0.006   -0.006
## 786     Im18 ~~   COM_A3  0.057 -0.009  -0.009   -0.013   -0.013
## 787     Im16 ~~   COM_A2  0.056  0.009   0.009    0.013    0.013
## 788      Im4 ~~    SAT_2  0.055 -0.004  -0.004   -0.020   -0.020
## 789     DECO =~   COM_A1  0.055 -0.009  -0.011   -0.007   -0.007
## 790       RI =~    C_CR1  0.054 -0.024  -0.014   -0.007   -0.007
## 791     Im14 ~~   COM_A1  0.054  0.004   0.004    0.017    0.017
## 792     Im10 ~~      Im1  0.054 -0.003  -0.003   -0.027   -0.027
## 793   COM_A2 ~~   C_REP1  0.052  0.005   0.005    0.012    0.012
## 794     Im20 ~~    C_CR1  0.050 -0.012  -0.012   -0.014   -0.014
## 795       RI =~      Im3  0.041  0.009   0.005    0.004    0.004
## 796     Im14 ~~    C_CR3  0.040  0.005   0.005    0.016    0.016
## 797    SAT_1 ~~   C_REP1  0.040  0.003   0.003    0.012    0.012
## 798    BRAND =~    C_CR3  0.039 -0.010  -0.012   -0.006   -0.006
## 799       RI =~    SAT_1  0.038  0.011   0.006    0.006    0.006
## 800    AFCOM =~    C_CR1  0.037  0.010   0.011    0.006    0.006
## 801      Im6 ~~   COM_A4  0.035 -0.007  -0.007   -0.010   -0.010
## 802     FOOD ~~    AFCOM  0.035  0.005   0.007    0.007    0.007
## 803      SAT =~   C_REP2  0.034 -0.004  -0.003   -0.005   -0.005
## 804    SAT_3 ~~   C_REP2  0.034 -0.003  -0.003   -0.016   -0.016
## 805 PRODQUAL =~   COM_A4  0.032 -0.013  -0.009   -0.006   -0.006
## 806     Im20 ~~    C_CR4  0.031 -0.010  -0.010   -0.010   -0.010
## 807     Im18 ~~    SAT_2  0.030  0.004   0.004    0.010    0.010
## 808     Im18 ~~   COM_A4  0.030 -0.006  -0.006   -0.009   -0.009
## 809     DECO =~      Im2  0.026  0.005   0.006    0.005    0.005
## 810     DECO =~      Im1  0.026 -0.006  -0.007   -0.005   -0.005
## 811     Im14 ~~     Im19  0.026  0.002   0.002    0.014    0.014
## 812     PROF  ~    AFCOM  0.026  0.006   0.007    0.007    0.007
## 813    BRAND ~~      SAT  0.025  0.005   0.006    0.006    0.006
## 814   C_REP1 ~~    C_CR4  0.024  0.004   0.004    0.008    0.008
## 815      Im3 ~~    SAT_3  0.024 -0.004  -0.004   -0.009   -0.009
## 816     Im18 ~~    C_CR1  0.022  0.006   0.006    0.009    0.009
## 817     PROF =~     Im10  0.021  0.005   0.005    0.005    0.005
## 818     PROF =~     Im14  0.021 -0.005  -0.005   -0.006   -0.006
## 819     Im19 ~~   C_REP3  0.021 -0.002  -0.002   -0.008   -0.008
## 820     Im19 ~~   COM_A2  0.020 -0.005  -0.005   -0.009   -0.009
## 821       RI =~    SAT_3  0.020  0.011   0.006    0.006    0.006
## 822    BRAND ~~    AFCOM  0.020 -0.006  -0.005   -0.005   -0.005
## 823       RI =~    C_CR4  0.019 -0.015  -0.009   -0.004   -0.004
## 824      Im1 ~~     Im19  0.019 -0.003  -0.003   -0.017   -0.017
## 825      Im1 ~~    C_CR4  0.018 -0.005  -0.005   -0.015   -0.015
## 826     Im12 ~~      Im1  0.018 -0.003  -0.003   -0.017   -0.017
## 827     Im11 ~~    SAT_3  0.018 -0.005  -0.005   -0.006   -0.006
## 828   FRENCH =~      Im4  0.018  0.004   0.004    0.003    0.003
## 829     DECO =~     Im14  0.018  0.003   0.003    0.004    0.004
## 830     DECO =~     Im10  0.018 -0.003  -0.003   -0.004   -0.004
## 831      Im5 ~~   C_REP3  0.015 -0.002  -0.002   -0.006   -0.006
## 832     Im19 ~~   COM_A4  0.014 -0.004  -0.004   -0.007   -0.007
## 833   CHOICE =~   COM_A2  0.013 -0.004  -0.005   -0.003   -0.003
## 834   C_REP2 ~~    C_CR1  0.012  0.002   0.002    0.011    0.011
## 835   C_REP1 ~~    C_CR1  0.012  0.003   0.003    0.006    0.006
## 836    AFCOM =~      Im3  0.012 -0.003  -0.003   -0.002   -0.002
## 837    AFCOM =~     Im22  0.012 -0.006  -0.006   -0.004   -0.004
## 838     Im18 ~~    C_CR4  0.012 -0.005  -0.005   -0.006   -0.006
## 839     FOOD =~     Im17  0.011  0.005   0.004    0.003    0.003
## 840     FOOD =~     Im18  0.011 -0.005  -0.004   -0.003   -0.003
## 841      Im2 ~~    SAT_3  0.010 -0.003  -0.003   -0.005   -0.005
## 842     Im13 ~~    SAT_1  0.010  0.002   0.002    0.007    0.007
## 843    SAT_1 ~~    SAT_2  0.009  0.005   0.005    0.017    0.017
## 844      Im1 ~~   C_REP1  0.009 -0.001  -0.001   -0.009   -0.009
## 845      Im3 ~~     Im16  0.008 -0.002  -0.002   -0.005   -0.005
## 846      COI =~     Im21  0.008  0.002   0.004    0.003    0.003
## 847     Im21 ~~   COM_A3  0.008 -0.004  -0.004   -0.005   -0.005
## 848   CHOICE =~      Im7  0.007  0.003   0.003    0.003    0.003
## 849   COM_A3 ~~    C_CR1  0.007  0.005   0.005    0.005    0.005
## 850   FRENCH  ~    AFCOM  0.006  0.006   0.007    0.007    0.007
## 851     Im11 ~~     Im16  0.006 -0.003  -0.003   -0.004   -0.004
## 852   COM_A2 ~~   C_REP2  0.006  0.001   0.001    0.007    0.007
## 853      Im3 ~~     Im21  0.005 -0.002  -0.002   -0.004   -0.004
## 854    SAT_2 ~~    C_CR4  0.005  0.003   0.003    0.004    0.004
## 855   COM_A4 ~~   C_REP2  0.005 -0.001  -0.001   -0.007   -0.007
## 856 PRODQUAL ~~      SAT  0.004 -0.001  -0.003   -0.003   -0.003
## 857     Im21 ~~      Im6  0.003 -0.002  -0.002   -0.003   -0.003
## 858     Im13 ~~   C_REP3  0.003  0.001   0.001    0.003    0.003
## 859     Im16 ~~     Im17  0.003 -0.001  -0.001   -0.006   -0.006
## 860   COM_A2 ~~    C_CR3  0.003 -0.003  -0.003   -0.003   -0.003
## 861     FOOD =~    SAT_1  0.003 -0.002  -0.002   -0.002   -0.002
## 862   FRENCH =~     Im10  0.002  0.002   0.002    0.002    0.002
## 863   FRENCH =~     Im14  0.002 -0.002  -0.002   -0.002   -0.002
## 864     Im22 ~~    C_CR4  0.002  0.003   0.003    0.003    0.003
## 865     Im16 ~~    C_CR3  0.002 -0.002  -0.002   -0.003   -0.003
## 866 PRODQUAL =~      Im3  0.002  0.002   0.001    0.001    0.001
## 867 PRODQUAL =~     Im21  0.001  0.002   0.002    0.001    0.001
## 868      Im6 ~~    C_CR3  0.001 -0.001  -0.001   -0.002   -0.002
## 869    BRAND =~   C_REP2  0.001  0.000   0.001    0.001    0.001
## 870 PRODQUAL =~    SAT_3  0.000 -0.001  -0.001   -0.001   -0.001
## 871      COI =~     Im18  0.000  0.000  -0.001   -0.001   -0.001
## 872      COI =~     Im17  0.000  0.000   0.001    0.001    0.001
## 873      Im4 ~~    SAT_3  0.000  0.000   0.000   -0.001   -0.001
## 874      Im2 ~~   COM_A2  0.000  0.000   0.000   -0.001   -0.001
## 875     Im13 ~~    C_CR4  0.000  0.001   0.001    0.001    0.001
## 876   FRENCH =~   C_REP3  0.000  0.000   0.000    0.000    0.000
## 877     Im19 ~~   COM_A3  0.000  0.000   0.000    0.001    0.001
## 878     Im18 ~~    SAT_3  0.000  0.000   0.000   -0.001   -0.001
## 879     FOOD =~     Im12  0.000  0.000   0.000    0.000    0.000
## 880   FRENCH =~     Im19  0.000  0.000   0.000    0.000    0.000
## 881    BRAND =~   COM_A1  0.000  0.000   0.000    0.000    0.000
## 882     DECO =~    C_CR3  0.000  0.000   0.000    0.000    0.000
## 883     FOOD =~   C_REP3  0.000  0.000   0.000    0.000    0.000
## 884     Im11 ~~   COM_A4  0.000  0.000   0.000    0.000    0.000
## 885      Im5 ~~     Im13  0.000  0.000   0.000    0.000    0.000
## 886    AFCOM =~     Im21  0.000  0.000   0.000    0.000    0.000

2.4.4 full model

# missing Im8, Im15, Im9

# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2  
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# 
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
# 
# SAT ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# AFCOM ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# "

# delete relationships based on regression significance levels
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2  
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7

AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4

SAT ~ DECO + CHOICE + PROF
AFCOM ~ ATMOS + PRODQUAL + FRENCH

RI ~ SAT + AFCOM + DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
COI ~ SAT + AFCOM + DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
"

# delete relationships based on regression significance levels
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2  
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7

AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4

SAT ~ DECO + CHOICE + PROF
AFCOM ~ ATMOS + PRODQUAL + FRENCH

RI ~ SAT + AFCOM + ATMOS + PRODQUAL + Im8 + Im9
COI ~ SAT + AFCOM + ATMOS + PRODQUAL
"

2.4.5 linear regression

# # linear regression
# lm_SAT_1 <-  lm (model_SAT_1, data = survey) 
# summary(lm_SAT_1)
# # note: lm deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.6 path analysis

# path analysis
SEM_fit <- cfa(model_SEM, data=survey, missing="ML")
summary(SEM_fit, fit.measures=TRUE, standardized=TRUE)
## lavaan 0.6.15 ended normally after 144 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       141
## 
##                                                   Used       Total
##   Number of observations                           533         553
##   Number of missing patterns                       124            
## 
## Model Test User Model:
##                                                       
##   Test statistic                              1498.168
##   Degrees of freedom                               483
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             12419.016
##   Degrees of freedom                               560
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.914
##   Tucker-Lewis Index (TLI)                       0.901
##                                                       
##   Robust Comparative Fit Index (CFI)             0.916
##   Robust Tucker-Lewis Index (TLI)                0.902
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -21618.793
##   Loglikelihood unrestricted model (H1)     -20869.709
##                                                       
##   Akaike (AIC)                               43519.587
##   Bayesian (BIC)                             44122.858
##   Sample-size adjusted Bayesian (SABIC)      43675.281
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.063
##   90 Percent confidence interval - lower         0.059
##   90 Percent confidence interval - upper         0.066
##   P-value H_0: RMSEA <= 0.050                    0.000
##   P-value H_0: RMSEA >= 0.080                    0.000
##                                                       
##   Robust RMSEA                                   0.063
##   90 Percent confidence interval - lower         0.060
##   90 Percent confidence interval - upper         0.067
##   P-value H_0: Robust RMSEA <= 0.050             0.000
##   P-value H_0: Robust RMSEA >= 0.080             0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.114
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.239    0.936
##     Im4               1.059    0.025   41.738    0.000    1.313    0.970
##     Im5               0.816    0.035   23.254    0.000    1.011    0.757
##   FOOD =~                                                               
##     Im10              1.000                               0.819    0.926
##     Im14              1.009    0.036   28.089    0.000    0.827    0.950
##   ATMOS =~                                                              
##     Im20              1.000                               1.258    0.842
##     Im21              0.859    0.042   20.623    0.000    1.081    0.787
##     Im22              1.073    0.047   23.068    0.000    1.350    0.881
##   PRODQUAL =~                                                           
##     Im11              1.000                               0.718    0.624
##     Im12              1.387    0.091   15.220    0.000    0.995    0.875
##     Im13              1.453    0.102   14.222    0.000    1.043    0.861
##   CHOICE =~                                                             
##     Im1               1.000                               1.303    0.978
##     Im2               0.886    0.032   27.629    0.000    1.154    0.899
##   PROF =~                                                               
##     Im16              1.000                               0.921    0.764
##     Im19              1.040    0.058   17.940    0.000    0.958    0.845
##   BRAND =~                                                              
##     Im17              1.000                               1.214    0.968
##     Im18              0.994    0.041   24.002    0.000    1.207    0.858
##   FRENCH =~                                                             
##     Im6               1.000                               0.978    0.815
##     Im7               1.190    0.068   17.374    0.000    1.163    0.956
##   AFCOM =~                                                              
##     COM_A1            1.000                               1.140    0.796
##     COM_A2            1.175    0.056   21.132    0.000    1.340    0.835
##     COM_A3            1.161    0.059   19.600    0.000    1.323    0.816
##     COM_A4            1.296    0.063   20.428    0.000    1.478    0.847
##   SAT =~                                                                
##     SAT_1             1.000                               0.880    0.863
##     SAT_2             0.937    0.051   18.427    0.000    0.825    0.818
##     SAT_3             0.819    0.056   14.748    0.000    0.720    0.634
##   RI =~                                                                 
##     C_REP1            1.000                               0.598    0.811
##     C_REP2            0.976    0.044   22.027    0.000    0.584    0.937
##     C_REP3            0.709    0.038   18.806    0.000    0.424    0.763
##   COI =~                                                                
##     C_CR1             1.000                               1.688    0.852
##     C_CR3             1.036    0.052   19.952    0.000    1.749    0.833
##     C_CR4             0.960    0.050   19.383    0.000    1.619    0.808
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   SAT ~                                                                 
##     DECO             -0.078    0.045   -1.730    0.084   -0.110   -0.110
##     CHOICE            0.115    0.040    2.903    0.004    0.171    0.171
##     PROF              0.562    0.083    6.764    0.000    0.589    0.589
##   AFCOM ~                                                               
##     ATMOS             0.417    0.049    8.561    0.000    0.460    0.460
##     PRODQUAL         -0.021    0.079   -0.263    0.792   -0.013   -0.013
##     FRENCH            0.234    0.055    4.275    0.000    0.200    0.200
##   RI ~                                                                  
##     SAT               0.177    0.036    4.861    0.000    0.261    0.261
##     AFCOM             0.180    0.030    6.035    0.000    0.343    0.343
##     ATMOS             0.034    0.026    1.289    0.197    0.072    0.072
##     PRODQUAL          0.099    0.045    2.215    0.027    0.118    0.118
##     Im8               0.031    0.025    1.202    0.229    0.051    0.054
##     Im9              -0.047    0.021   -2.295    0.022   -0.079   -0.107
##   COI ~                                                                 
##     SAT              -0.492    0.110   -4.488    0.000   -0.256   -0.256
##     AFCOM             0.515    0.090    5.725    0.000    0.348    0.348
##     ATMOS             0.107    0.083    1.293    0.196    0.080    0.080
##     PRODQUAL          0.079    0.130    0.608    0.543    0.034    0.034
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FOOD              0.422    0.051    8.233    0.000    0.416    0.416
##     ATMOS             0.733    0.083    8.803    0.000    0.470    0.470
##     PRODQUAL          0.416    0.052    7.931    0.000    0.468    0.468
##     CHOICE            0.725    0.081    9.006    0.000    0.449    0.449
##     PROF              0.759    0.072   10.490    0.000    0.665    0.665
##     BRAND             0.784    0.078   10.009    0.000    0.521    0.521
##     FRENCH            0.418    0.065    6.479    0.000    0.345    0.345
##   FOOD ~~                                                               
##     ATMOS             0.303    0.052    5.850    0.000    0.294    0.294
##     PRODQUAL          0.270    0.035    7.669    0.000    0.459    0.459
##     CHOICE            0.319    0.051    6.253    0.000    0.299    0.299
##     PROF              0.394    0.045    8.821    0.000    0.522    0.522
##     BRAND             0.327    0.048    6.754    0.000    0.329    0.329
##     FRENCH            0.470    0.048    9.833    0.000    0.586    0.586
##   ATMOS ~~                                                              
##     PRODQUAL          0.381    0.054    7.029    0.000    0.422    0.422
##     CHOICE            0.743    0.086    8.681    0.000    0.453    0.453
##     PROF              0.569    0.069    8.217    0.000    0.491    0.491
##     BRAND             0.791    0.083    9.581    0.000    0.518    0.518
##     FRENCH            0.416    0.065    6.356    0.000    0.338    0.338
##   PRODQUAL ~~                                                           
##     CHOICE            0.456    0.056    8.207    0.000    0.487    0.487
##     PROF              0.361    0.045    8.058    0.000    0.546    0.546
##     BRAND             0.495    0.055    8.998    0.000    0.568    0.568
##     FRENCH            0.220    0.039    5.688    0.000    0.314    0.314
##   CHOICE ~~                                                             
##     PROF              0.733    0.073   10.028    0.000    0.611    0.611
##     BRAND             0.827    0.081   10.226    0.000    0.523    0.523
##     FRENCH            0.284    0.061    4.621    0.000    0.223    0.223
##   PROF ~~                                                               
##     BRAND             0.688    0.068   10.138    0.000    0.615    0.615
##     FRENCH            0.363    0.053    6.849    0.000    0.403    0.403
##   BRAND ~~                                                              
##     FRENCH            0.392    0.063    6.234    0.000    0.330    0.330
##  .RI ~~                                                                 
##    .COI              -0.019    0.039   -0.495    0.621   -0.026   -0.026
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.991    0.058   86.549    0.000    4.991    3.769
##    .Im4               4.997    0.059   84.903    0.000    4.997    3.690
##    .Im5               5.040    0.059   86.082    0.000    5.040    3.775
##    .Im10              6.094    0.038  158.635    0.000    6.094    6.886
##    .Im14              6.134    0.038  161.799    0.000    6.134    7.045
##    .Im20              4.698    0.065   72.346    0.000    4.698    3.145
##    .Im21              5.158    0.060   86.498    0.000    5.158    3.756
##    .Im22              4.299    0.067   64.388    0.000    4.299    2.806
##    .Im11              5.654    0.050  112.746    0.000    5.654    4.917
##    .Im12              5.665    0.050  114.079    0.000    5.665    4.978
##    .Im13              5.448    0.053  103.321    0.000    5.448    4.499
##    .Im1               4.799    0.058   82.888    0.000    4.799    3.603
##    .Im2               4.867    0.056   87.173    0.000    4.867    3.793
##    .Im16              5.153    0.053   97.535    0.000    5.153    4.273
##    .Im19              5.152    0.049  104.263    0.000    5.152    4.541
##    .Im17              5.035    0.055   92.303    0.000    5.035    4.015
##    .Im18              4.598    0.061   74.786    0.000    4.598    3.271
##    .Im6               5.821    0.052  111.587    0.000    5.821    4.849
##    .Im7               5.753    0.053  108.247    0.000    5.753    4.726
##    .COM_A1            4.298    0.062   68.859    0.000    4.298    2.998
##    .COM_A2            3.899    0.070   55.887    0.000    3.899    2.431
##    .COM_A3            3.548    0.071   50.168    0.000    3.548    2.188
##    .COM_A4            3.464    0.076   45.676    0.000    3.464    1.985
##    .SAT_1             5.349    0.044  120.874    0.000    5.349    5.246
##    .SAT_2             5.491    0.044  125.225    0.000    5.491    5.448
##    .SAT_3             5.469    0.050  108.319    0.000    5.469    4.813
##    .C_REP1            4.339    0.164   26.523    0.000    4.339    5.885
##    .C_REP2            4.566    0.159   28.732    0.000    4.566    7.330
##    .C_REP3            4.716    0.116   40.561    0.000    4.716    8.483
##    .C_CR1             2.687    0.086   31.062    0.000    2.687    1.356
##    .C_CR3             3.269    0.091   35.862    0.000    3.269    1.557
##    .C_CR4             2.787    0.087   31.941    0.000    2.787    1.390
##     DECO              0.000                               0.000    0.000
##     FOOD              0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     PRODQUAL          0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     PROF              0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
##    .AFCOM             0.000                               0.000    0.000
##    .SAT               0.000                               0.000    0.000
##    .RI                0.000                               0.000    0.000
##    .COI               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.218    0.025    8.639    0.000    0.218    0.124
##    .Im4               0.110    0.025    4.399    0.000    0.110    0.060
##    .Im5               0.761    0.051   14.998    0.000    0.761    0.427
##    .Im10              0.112    0.020    5.700    0.000    0.112    0.143
##    .Im14              0.074    0.019    3.849    0.000    0.074    0.098
##    .Im20              0.648    0.060   10.882    0.000    0.648    0.290
##    .Im21              0.718    0.057   12.536    0.000    0.718    0.381
##    .Im22              0.525    0.061    8.601    0.000    0.525    0.224
##    .Im11              0.807    0.055   14.558    0.000    0.807    0.610
##    .Im12              0.304    0.038    7.915    0.000    0.304    0.235
##    .Im13              0.379    0.044    8.614    0.000    0.379    0.258
##    .Im1               0.076    0.048    1.592    0.111    0.076    0.043
##    .Im2               0.316    0.042    7.478    0.000    0.316    0.192
##    .Im16              0.606    0.051   11.948    0.000    0.606    0.416
##    .Im19              0.369    0.044    8.424    0.000    0.369    0.286
##    .Im17              0.098    0.046    2.133    0.033    0.098    0.062
##    .Im18              0.520    0.056    9.354    0.000    0.520    0.263
##    .Im6               0.485    0.054    8.944    0.000    0.485    0.336
##    .Im7               0.129    0.064    2.015    0.044    0.129    0.087
##    .COM_A1            0.755    0.059   12.690    0.000    0.755    0.367
##    .COM_A2            0.778    0.067   11.631    0.000    0.778    0.302
##    .COM_A3            0.877    0.071   12.290    0.000    0.877    0.334
##    .COM_A4            0.859    0.077   11.232    0.000    0.859    0.282
##    .SAT_1             0.265    0.035    7.659    0.000    0.265    0.255
##    .SAT_2             0.336    0.034    9.751    0.000    0.336    0.331
##    .SAT_3             0.773    0.055   13.961    0.000    0.773    0.598
##    .C_REP1            0.186    0.016   11.386    0.000    0.186    0.342
##    .C_REP2            0.047    0.010    4.598    0.000    0.047    0.122
##    .C_REP3            0.129    0.009   13.827    0.000    0.129    0.419
##    .C_CR1             1.078    0.117    9.254    0.000    1.078    0.275
##    .C_CR3             1.346    0.133   10.153    0.000    1.346    0.306
##    .C_CR4             1.399    0.125   11.156    0.000    1.399    0.348
##     DECO              1.535    0.109   14.033    0.000    1.000    1.000
##     FOOD              0.671    0.051   13.154    0.000    1.000    1.000
##     ATMOS             1.583    0.138   11.457    0.000    1.000    1.000
##     PRODQUAL          0.515    0.069    7.420    0.000    1.000    1.000
##     CHOICE            1.697    0.119   14.261    0.000    1.000    1.000
##     PROF              0.849    0.088    9.600    0.000    1.000    1.000
##     BRAND             1.474    0.107   13.778    0.000    1.000    1.000
##     FRENCH            0.956    0.095   10.087    0.000    1.000    1.000
##    .AFCOM             0.900    0.091    9.904    0.000    0.692    0.692
##    .SAT               0.458    0.050    9.160    0.000    0.592    0.592
##    .RI                0.238    0.022   10.738    0.000    0.666    0.666
##    .COI               2.338    0.217   10.750    0.000    0.821    0.821
# note: cfa deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.6.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.4.6.2 local fit measures

# semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5, 
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
         rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
         nCharNodes = 7,shapeMan = "rectangle", 
         sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
         curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
         )

lambda = inspect(SEM_fit, what="std")$lambda
theta = inspect(SEM_fit, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones
2.4.6.2.1 Indicator reliability criterion
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail
##        DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI Im8
## Im3     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im4     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im5     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im10    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im14    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im20    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im21    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im22    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im11    NaN  NaN   NaN   0.39    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im12    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im13    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im1     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im2     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im16    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im19    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im17    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im18    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im6     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im7     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A4  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## SAT_1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## SAT_2   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## SAT_3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_REP1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_REP2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_REP3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_CR1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_CR3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_CR4   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im8     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im9     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
##        Im9
## Im3    NaN
## Im4    NaN
## Im5    NaN
## Im10   NaN
## Im14   NaN
## Im20   NaN
## Im21   NaN
## Im22   NaN
## Im11   NaN
## Im12   NaN
## Im13   NaN
## Im1    NaN
## Im2    NaN
## Im16   NaN
## Im19   NaN
## Im17   NaN
## Im18   NaN
## Im6    NaN
## Im7    NaN
## COM_A1 NaN
## COM_A2 NaN
## COM_A3 NaN
## COM_A4 NaN
## SAT_1  NaN
## SAT_2  NaN
## SAT_3  NaN
## C_REP1 NaN
## C_REP2 NaN
## C_REP3 NaN
## C_CR1  NaN
## C_CR3  NaN
## C_CR4  NaN
## Im8    NaN
## Im9    NaN
2.4.6.2.2 Construct reliability criterion
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im8       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im9       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
##          Im8 Im9
## DECO     NaN NaN
## FOOD     NaN NaN
## ATMOS    NaN NaN
## PRODQUAL NaN NaN
## CHOICE   NaN NaN
## PROF     NaN NaN
## BRAND    NaN NaN
## FRENCH   NaN NaN
## AFCOM    NaN NaN
## SAT      NaN NaN
## RI       NaN NaN
## COI      NaN NaN
## Im8      NaN NaN
## Im9      NaN NaN
2.4.6.2.3 Average Variance Extracted criterion
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail
##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im8       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im9       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
##          Im8 Im9
## DECO     NaN NaN
## FOOD     NaN NaN
## ATMOS    NaN NaN
## PRODQUAL NaN NaN
## CHOICE   NaN NaN
## PROF     NaN NaN
## BRAND    NaN NaN
## FRENCH   NaN NaN
## AFCOM    NaN NaN
## SAT      NaN NaN
## RI       NaN NaN
## COI      NaN NaN
## Im8      NaN NaN
## Im9      NaN NaN
2.4.6.2.4 Fornell-Larcker Criteria
# correlations between constructs (factors...) should be lower than .7
psi = inspect(SEM_fit, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail
##           DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH AFCOM   SAT    RI
## DECO     1.000                                                               
## FOOD       NaN 1.000                                                         
## ATMOS      NaN   NaN 1.000                                                   
## PRODQUAL   NaN   NaN   NaN  1.000                                            
## CHOICE     NaN   NaN   NaN    NaN  1.000                                     
## PROF       NaN   NaN   NaN    NaN    NaN 1.000                               
## BRAND      NaN   NaN   NaN    NaN    NaN   NaN 1.000                         
## FRENCH     NaN   NaN   NaN    NaN    NaN   NaN   NaN  1.000                  
## AFCOM      NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN            
## SAT        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN      
## RI         NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
## COI        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
## Im8        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
## Im9        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
##            COI   Im8   Im9
## DECO                      
## FOOD                      
## ATMOS                     
## PRODQUAL                  
## CHOICE                    
## PROF                      
## BRAND                     
## FRENCH                    
## AFCOM                     
## SAT                       
## RI                        
## COI      0.821            
## Im8        NaN 1.000      
## Im9        NaN   NaN 1.000
# AVE should be higher than squared correlations between constructs

# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full
##               DECO      FOOD     ATMOS  PRODQUAL    CHOICE      PROF     BRAND
## DECO     0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## FOOD     0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## ATMOS    0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## PRODQUAL 0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## CHOICE   0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## PROF     0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## BRAND    0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## FRENCH   0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## AFCOM    0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## SAT      0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## RI       0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## COI      0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## Im8      0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
## Im9      0.7962407 0.8795455 0.7017213 0.6320711 0.8827046 0.6485812 0.8372868
##             FRENCH     AFCOM       SAT       RI       COI Im8 Im9
## DECO     0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## FOOD     0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## ATMOS    0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## PRODQUAL 0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## CHOICE   0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## PROF     0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## BRAND    0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## FRENCH   0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## AFCOM    0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## SAT      0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## RI       0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## COI      0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## Im8      0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
## Im9      0.7883715 0.6786044 0.6052217 0.705655 0.6906007   1   1
psi
##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH  AFCOM    SAT
## DECO      1.000                                                               
## FOOD      0.416  1.000                                                        
## ATMOS     0.470  0.294  1.000                                                 
## PRODQUAL  0.468  0.459  0.422  1.000                                          
## CHOICE    0.449  0.299  0.453  0.487  1.000                                   
## PROF      0.665  0.522  0.491  0.546  0.611  1.000                            
## BRAND     0.521  0.329  0.518  0.568  0.523  0.615  1.000                     
## FRENCH    0.345  0.586  0.338  0.314  0.223  0.403  0.330  1.000              
## AFCOM     0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.692       
## SAT       0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.592
## RI        0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
## COI       0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
## Im8       0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
## Im9       0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
##              RI    COI    Im8    Im9
## DECO                                
## FOOD                                
## ATMOS                               
## PRODQUAL                            
## CHOICE                              
## PROF                                
## BRAND                               
## FRENCH                              
## AFCOM                               
## SAT                                 
## RI        0.666                     
## COI      -0.026  0.821              
## Im8       0.000  0.000  1.000       
## Im9       0.000  0.000  0.428  1.000
AVEpsi_fail
##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH  AFCOM    SAT
## DECO          .                                                               
## FOOD        NaN      .                                                        
## ATMOS       NaN    NaN      .                                                 
## PRODQUAL    NaN    NaN    NaN      .                                          
## CHOICE      NaN    NaN    NaN    NaN      .                                   
## PROF        NaN    NaN    NaN    NaN    NaN      .                            
## BRAND       NaN    NaN    NaN    NaN    NaN    NaN      .                     
## FRENCH      NaN    NaN    NaN    NaN    NaN    NaN    NaN      .              
## AFCOM       NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .       
## SAT         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .
## RI          NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## COI         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## Im8         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## Im9         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
##              RI    COI    Im8    Im9
## DECO                                
## FOOD                                
## ATMOS                               
## PRODQUAL                            
## CHOICE                              
## PROF                                
## BRAND                               
## FRENCH                              
## AFCOM                               
## SAT                                 
## RI            .                     
## COI         NaN      .              
## Im8         NaN    NaN      .       
## Im9         NaN    NaN    NaN      .

2.4.6.3 Modification indices

arrange(modificationindices(SEM_fit),-mi)
##          lhs op      rhs      mi    epc sepc.lv sepc.all sepc.nox
## 1        Im8  ~   FRENCH 148.977  0.541   0.529    0.498    0.498
## 2        Im9  ~ PRODQUAL  69.443  0.658   0.472    0.348    0.348
## 3     FRENCH  ~      Im8  65.342  0.276   0.282    0.299    0.282
## 4      AFCOM =~   C_REP1  56.927  0.175   0.200    0.271    0.271
## 5        Im8  ~     PROF  52.904  0.355   0.327    0.308    0.308
## 6     C_REP2 ~~   C_REP3  51.322  0.103   0.103    1.310    1.310
## 7     FRENCH  ~      Im9  47.927  0.185   0.189    0.256    0.189
## 8        Im8  ~       RI  47.096  0.870   0.520    0.490    0.490
## 9      AFCOM  ~      SAT  42.072  0.406   0.313    0.313    0.313
## 10       Im9  ~       RI  41.721  1.046   0.625    0.461    0.461
## 11       SAT  ~    AFCOM  41.538  0.223   0.289    0.289    0.289
## 12       Im9  ~   FRENCH  36.054  0.340   0.332    0.245    0.245
## 13     AFCOM ~~      SAT  35.327  0.216   0.336    0.336    0.336
## 14       Im9  ~     PROF  34.586  0.366   0.338    0.249    0.249
## 15       Im9  ~    ATMOS  34.005  0.261   0.328    0.242    0.242
## 16       Im8  ~      SAT  32.572  0.291   0.256    0.241    0.241
## 17    COM_A1 ~~   COM_A2  29.181  0.277   0.277    0.362    0.362
## 18       Im8  ~     DECO  28.249  0.182   0.226    0.213    0.213
## 19       Im9  ~     DECO  27.501  0.230   0.285    0.210    0.210
## 20       Im9  ~   CHOICE  27.251  0.217   0.283    0.209    0.209
## 21       SAT  ~      COI  25.576  0.191   0.367    0.367    0.367
## 22       Im8  ~    AFCOM  25.175  0.193   0.220    0.207    0.207
## 23     AFCOM  ~       RI  25.070  1.305   0.684    0.684    0.684
## 24     ATMOS =~   C_REP1  22.621  0.095   0.120    0.163    0.163
## 25       SAT  ~       RI  19.558  0.478   0.325    0.325    0.325
## 26      Im11 ~~     Im13  19.309 -0.182  -0.182   -0.329   -0.329
## 27     BRAND =~     Im13  19.265  0.195   0.237    0.196    0.196
## 28        RI =~    SAT_2  18.147  0.269   0.161    0.159    0.159
## 29       Im8  ~    ATMOS  17.170  0.145   0.182    0.172    0.172
## 30       Im9  ~      SAT  16.327  0.263   0.231    0.171    0.171
## 31       Im8  ~ PRODQUAL  16.114  0.248   0.178    0.168    0.168
## 32  PRODQUAL  ~      Im9  15.863  0.078   0.108    0.146    0.108
## 33     AFCOM =~   C_REP2  14.754 -0.076  -0.086   -0.138   -0.138
## 34       Im9  ~    AFCOM  14.613  0.188   0.214    0.158    0.158
## 35    CHOICE =~     Im20  14.151 -0.149  -0.194   -0.130   -0.130
## 36    C_REP1 ~~   C_REP3  13.846 -0.049  -0.049   -0.318   -0.318
## 37     BRAND =~     Im12  13.817 -0.157  -0.191   -0.168   -0.168
## 38    CHOICE =~     Im13  13.570  0.133   0.173    0.143    0.143
## 39      FOOD =~     Im11  13.181  0.220   0.180    0.157    0.157
## 40       SAT =~   COM_A3  12.896  0.209   0.184    0.114    0.114
## 41    COM_A3 ~~   C_REP1  12.775  0.078   0.078    0.194    0.194
## 42      Im21 ~~     Im22  12.609 -0.227  -0.227   -0.371   -0.371
## 43     AFCOM  ~      COI  12.576 -0.339  -0.502   -0.502   -0.502
## 44     AFCOM =~   C_REP3  12.429 -0.066  -0.075   -0.135   -0.135
## 45      PROF =~   COM_A3  12.311  0.205   0.189    0.117    0.117
## 46        RI =~     Im22  12.287 -0.297  -0.178   -0.116   -0.116
## 47      Im21 ~~   C_REP3  12.056  0.055   0.055    0.181    0.181
## 48       SAT  ~   FRENCH  11.740  0.147   0.164    0.164    0.164
## 49    C_REP1 ~~   C_REP2  11.386 -0.076  -0.076   -0.806   -0.806
## 50     AFCOM =~    SAT_2  11.117  0.096   0.110    0.109    0.109
## 51      Im11 ~~     Im12  10.969  0.130   0.130    0.263    0.263
## 52    COM_A3 ~~   COM_A4  10.678  0.209   0.209    0.241    0.241
## 53      Im13 ~~      Im1  10.509  0.067   0.067    0.395    0.395
## 54    COM_A1 ~~   COM_A4  10.381 -0.180  -0.180   -0.224   -0.224
## 55  PRODQUAL =~    C_CR4  10.238  0.291   0.209    0.104    0.104
## 56     ATMOS =~   C_REP3   9.953 -0.051  -0.064   -0.115   -0.115
## 57    CHOICE =~   C_REP3   9.780 -0.044  -0.058   -0.104   -0.104
## 58     ATMOS =~     Im12   9.634 -0.107  -0.135   -0.119   -0.119
## 59       SAT =~    C_CR4   9.519  0.235   0.206    0.103    0.103
## 60     AFCOM  ~     PROF   9.470  0.236   0.190    0.190    0.190
## 61     AFCOM =~     Im11   9.462  0.122   0.139    0.121    0.121
## 62    CHOICE =~   C_REP1   9.375  0.053   0.069    0.094    0.094
## 63    CHOICE =~     Im12   9.305 -0.104  -0.136   -0.119   -0.119
## 64        RI =~   COM_A1   9.208  0.264   0.158    0.110    0.110
## 65    FRENCH =~   C_REP1   9.136  0.070   0.068    0.092    0.092
## 66      Im13 ~~     Im17   8.862  0.067   0.067    0.347    0.347
## 67     ATMOS =~    C_CR4   8.825  0.157   0.198    0.099    0.099
## 68       COI =~    SAT_2   8.803  0.060   0.101    0.100    0.100
## 69       Im4 ~~     Im17   8.688 -0.046  -0.046   -0.441   -0.441
## 70      DECO =~   COM_A3   8.647  0.119   0.147    0.091    0.091
## 71        RI =~     Im21   8.642  0.239   0.143    0.104    0.104
## 72      PROF ~~      SAT   8.611 -0.148  -0.238   -0.238   -0.238
## 73      PROF  ~      SAT   8.611 -0.323  -0.309   -0.309   -0.309
## 74      Im16 ~~     Im19   8.611  0.274   0.274    0.580    0.580
## 75     AFCOM  ~   CHOICE   8.529  0.129   0.148    0.148    0.148
## 76      Im19 ~~   C_REP1   8.476 -0.046  -0.046   -0.175   -0.175
## 77  PRODQUAL =~    C_CR1   8.437 -0.255  -0.183   -0.092   -0.092
## 78       COI =~   C_REP1   8.348  0.038   0.065    0.088    0.088
## 79     BRAND =~   COM_A3   7.914  0.118   0.143    0.088    0.088
## 80       Im1 ~~    SAT_2   7.882 -0.052  -0.052   -0.327   -0.327
## 81       SAT =~   C_REP1   7.874  0.082   0.072    0.098    0.098
## 82      DECO =~   C_REP1   7.696  0.050   0.062    0.085    0.085
## 83     BRAND =~     Im20   7.612 -0.126  -0.153   -0.103   -0.103
## 84      Im10 ~~      Im6   7.456 -0.039  -0.039   -0.168   -0.168
## 85      DECO =~    C_CR1   7.446 -0.129  -0.160   -0.081   -0.081
## 86       SAT  ~      Im8   7.339  0.089   0.101    0.107    0.101
## 87      FOOD =~      Im6   7.298 -0.292  -0.239   -0.199   -0.199
## 88      Im10 ~~     Im16   7.288  0.044   0.044    0.171    0.171
## 89      DECO  ~      SAT   7.220 -0.759  -0.539   -0.539   -0.539
## 90      DECO ~~      SAT   7.219 -0.348  -0.415   -0.415   -0.415
## 91      Im22 ~~   C_REP3   6.968 -0.042  -0.042   -0.159   -0.159
## 92     ATMOS =~     Im11   6.798  0.104   0.131    0.114    0.114
## 93      Im10 ~~   COM_A2   6.726  0.048   0.048    0.163    0.163
## 94      PROF =~   C_REP3   6.688 -0.058  -0.053   -0.095   -0.095
## 95  PRODQUAL  ~    AFCOM   6.645 -0.138  -0.220   -0.220   -0.220
## 96  PRODQUAL ~~    AFCOM   6.645 -0.125  -0.183   -0.183   -0.183
## 97       SAT =~     Im12   6.621 -0.116  -0.102   -0.089   -0.089
## 98  PRODQUAL =~      Im5   6.620  0.178   0.128    0.096    0.096
## 99     BRAND =~      Im4   6.443 -0.070  -0.085   -0.063   -0.063
## 100    BRAND =~      Im5   6.363  0.102   0.124    0.093    0.093
## 101   COM_A4 ~~    SAT_1   6.326  0.079   0.079    0.166    0.166
## 102     Im14 ~~     Im16   6.245 -0.040  -0.040   -0.190   -0.190
## 103    ATMOS =~      Im5   6.199  0.097   0.122    0.092    0.092
## 104    BRAND =~    C_CR4   6.111  0.127   0.154    0.077    0.077
## 105   CHOICE =~      Im5   6.096  0.088   0.114    0.085    0.085
## 106      Im3 ~~      Im1   6.025 -0.036  -0.036   -0.283   -0.283
## 107     Im20 ~~     Im21   6.010  0.144   0.144    0.211    0.211
## 108    BRAND =~     Im22   5.904  0.113   0.138    0.090    0.090
## 109     FOOD =~      Im7   5.896  0.317   0.260    0.213    0.213
## 110      Im8  ~   CHOICE   5.883  0.079   0.103    0.097    0.097
## 111     DECO =~   C_REP3   5.867 -0.036  -0.044   -0.080   -0.080
## 112    ATMOS ~~    AFCOM   5.814 -0.271  -0.227   -0.227   -0.227
## 113    ATMOS  ~    AFCOM   5.814 -0.301  -0.273   -0.273   -0.273
## 114     FOOD =~   COM_A3   5.718  0.146   0.120    0.074    0.074
## 115   FRENCH =~     Im16   5.701 -0.123  -0.120   -0.100   -0.100
## 116     DECO =~     Im20   5.680 -0.101  -0.125   -0.083   -0.083
## 117       RI =~     Im12   5.663 -0.151  -0.090   -0.080   -0.080
## 118    AFCOM =~     Im12   5.635 -0.077  -0.088   -0.077   -0.077
## 119    BRAND =~      Im7   5.634 -0.095  -0.115   -0.094   -0.094
## 120   COM_A2 ~~   COM_A3   5.414 -0.136  -0.136   -0.165   -0.165
## 121     FOOD =~     Im13   5.366 -0.129  -0.106   -0.088   -0.088
## 122      Im3 ~~     Im22   5.358  0.052   0.052    0.154    0.154
## 123    BRAND =~   C_REP3   5.350 -0.036  -0.043   -0.078   -0.078
## 124     Im10 ~~     Im13   5.337 -0.033  -0.033   -0.159   -0.159
## 125     FOOD =~   C_REP1   5.307  0.063   0.051    0.070    0.070
## 126     Im20 ~~     Im17   5.301 -0.062  -0.062   -0.248   -0.248
## 127    ATMOS =~      Im4   5.284 -0.060  -0.075   -0.055   -0.055
## 128     Im10 ~~      Im7   5.277  0.034   0.034    0.286    0.286
## 129      Im3 ~~      Im5   5.276 -0.077  -0.077   -0.190   -0.190
## 130     DECO =~      Im7   5.227 -0.090  -0.112   -0.092   -0.092
## 131     PROF =~    C_CR4   5.213  0.162   0.149    0.074    0.074
## 132     PROF =~    C_CR1   5.213 -0.155  -0.143   -0.072   -0.072
## 133     DECO =~     Im17   5.203 -0.100  -0.125   -0.099   -0.099
## 134     DECO =~     Im18   5.203  0.100   0.124    0.088    0.088
## 135   FRENCH =~     Im22   5.112  0.115   0.113    0.073    0.073
## 136      Im3 ~~      Im4   5.059  0.165   0.165    1.065    1.065
## 137     Im13 ~~      Im2   4.995 -0.046  -0.046   -0.133   -0.133
## 138      Im4 ~~    C_CR1   4.985 -0.067  -0.067   -0.196   -0.196
## 139    BRAND =~      Im6   4.973  0.075   0.091    0.076    0.076
## 140   FRENCH  ~      SAT   4.845  0.142   0.128    0.128    0.128
## 141   FRENCH ~~      SAT   4.845  0.065   0.098    0.098    0.098
## 142   FRENCH =~   C_REP2   4.813 -0.038  -0.037   -0.060   -0.060
## 143    SAT_1 ~~    SAT_3   4.812  0.088   0.088    0.195    0.195
## 144     DECO =~    C_CR4   4.807  0.109   0.135    0.067    0.067
## 145      Im4 ~~     Im18   4.801  0.041   0.041    0.171    0.171
## 146     Im22 ~~      Im1   4.757  0.055   0.055    0.273    0.273
## 147     PROF =~     Im12   4.747 -0.130  -0.120   -0.105   -0.105
## 148   CHOICE =~   COM_A3   4.744  0.082   0.107    0.066    0.066
## 149    SAT_2 ~~    SAT_3   4.724 -0.082  -0.082   -0.162   -0.162
## 150     Im20 ~~      Im6   4.723 -0.068  -0.068   -0.121   -0.121
## 151    SAT_1 ~~   C_REP2   4.671 -0.023  -0.023   -0.201   -0.201
## 152     FOOD =~      Im5   4.664  0.121   0.099    0.074    0.074
## 153      Im5 ~~      Im6   4.639 -0.065  -0.065   -0.108   -0.108
## 154     FOOD =~    C_CR1   4.636 -0.155  -0.127   -0.064   -0.064
## 155     PROF =~      Im2   4.612  0.180   0.165    0.129    0.129
## 156     PROF =~      Im1   4.611 -0.203  -0.187   -0.140   -0.140
## 157    AFCOM =~     Im20   4.576 -0.107  -0.123   -0.082   -0.082
## 158     DECO =~      Im6   4.555  0.071   0.089    0.074    0.074
## 159    BRAND =~    C_CR1   4.542 -0.104  -0.126   -0.064   -0.064
## 160      SAT =~   C_REP2   4.505 -0.052  -0.046   -0.073   -0.073
## 161     Im13 ~~     Im16   4.490 -0.063  -0.063   -0.132   -0.132
## 162   C_REP2 ~~    C_CR4   4.482 -0.044  -0.044   -0.172   -0.172
## 163     PROF =~     Im20   4.462 -0.134  -0.123   -0.082   -0.082
## 164     DECO =~     Im22   4.431  0.090   0.112    0.073    0.073
## 165     Im11 ~~      Im6   4.425 -0.066  -0.066   -0.105   -0.105
## 166     Im19 ~~   C_REP2   4.382  0.024   0.024    0.184    0.184
## 167 PRODQUAL =~      Im2   4.350 -0.129  -0.092   -0.072   -0.072
## 168      Im1 ~~   C_REP3   4.334 -0.021  -0.021   -0.216   -0.216
## 169     PROF =~   C_REP1   4.281  0.057   0.052    0.071    0.071
## 170     Im11 ~~      Im1   4.276 -0.052  -0.052   -0.209   -0.209
## 171   COM_A3 ~~   C_REP2   4.258 -0.034  -0.034   -0.164   -0.164
## 172    AFCOM =~      Im5   4.257  0.080   0.091    0.068    0.068
## 173     DECO =~   COM_A2   4.251 -0.080  -0.099   -0.061   -0.061
## 174      SAT =~    C_CR1   4.232 -0.151  -0.133   -0.067   -0.067
## 175     Im22 ~~   C_REP1   4.228  0.039   0.039    0.126    0.126
## 176     Im22 ~~     Im11   4.197  0.078   0.078    0.120    0.120
## 177      COI  ~   FRENCH   4.171 -0.181  -0.105   -0.105   -0.105
## 178    AFCOM ~~      COI   4.171  0.698   0.481    0.481    0.481
## 179     Im20 ~~     Im13   4.169  0.064   0.064    0.130    0.130
## 180     PROF =~    SAT_2   4.082  0.123   0.113    0.112    0.112
## 181     Im22 ~~    SAT_3   4.074 -0.078  -0.078   -0.122   -0.122
## 182       RI =~     Im14   4.037  0.068   0.041    0.047    0.047
## 183   CHOICE  ~    AFCOM   4.032  0.105   0.092    0.092    0.092
## 184   CHOICE ~~    AFCOM   4.032  0.095   0.077    0.077    0.077
## 185 PRODQUAL =~      Im1   3.989  0.139   0.100    0.075    0.075
## 186      Im4 ~~      Im6   3.965  0.035   0.035    0.154    0.154
## 187     Im12 ~~      Im7   3.962  0.046   0.046    0.233    0.233
## 188     Im20 ~~   COM_A4   3.947  0.088   0.088    0.119    0.119
## 189     PROF =~    SAT_1   3.932 -0.126  -0.116   -0.114   -0.114
## 190   COM_A1 ~~    SAT_3   3.909  0.079   0.079    0.104    0.104
## 191     Im22 ~~   C_REP2   3.904 -0.028  -0.028   -0.179   -0.179
## 192     Im14 ~~   COM_A2   3.881 -0.036  -0.036   -0.148   -0.148
## 193     Im14 ~~    C_CR1   3.851 -0.045  -0.045   -0.160   -0.160
## 194     Im11 ~~   C_REP1   3.844  0.038   0.038    0.098    0.098
## 195    ATMOS =~   COM_A1   3.825 -0.087  -0.110   -0.077   -0.077
## 196       RI =~   COM_A2   3.794 -0.180  -0.108   -0.067   -0.067
## 197   FRENCH =~   COM_A3   3.791  0.106   0.104    0.064    0.064
## 198     Im20 ~~    SAT_1   3.777 -0.053  -0.053   -0.129   -0.129
## 199      Im4 ~~   COM_A3   3.773  0.048   0.048    0.155    0.155
## 200      SAT =~   COM_A2   3.770 -0.108  -0.095   -0.059   -0.059
## 201   COM_A1 ~~    SAT_1   3.723 -0.054  -0.054   -0.121   -0.121
## 202   FRENCH =~     Im20   3.722 -0.097  -0.095   -0.063   -0.063
## 203    SAT_3 ~~    C_CR3   3.694 -0.111  -0.111   -0.109   -0.109
## 204    SAT_2 ~~   C_REP1   3.694  0.027   0.027    0.109    0.109
## 205   FRENCH =~    C_CR1   3.690 -0.117  -0.114   -0.058   -0.058
## 206      SAT =~   COM_A4   3.661  0.114   0.100    0.057    0.057
## 207      Im1 ~~    SAT_1   3.661  0.035   0.035    0.247    0.247
## 208      Im4 ~~     Im11   3.648 -0.042  -0.042   -0.141   -0.141
## 209      SAT =~     Im13   3.582  0.091   0.080    0.066    0.066
## 210     PROF =~   COM_A2   3.573 -0.106  -0.098   -0.061   -0.061
## 211       RI =~      Im5   3.548  0.138   0.082    0.062    0.062
## 212    ATMOS =~   COM_A4   3.545  0.096   0.121    0.069    0.069
## 213     Im11 ~~     Im17   3.504 -0.050  -0.050   -0.178   -0.178
## 214 PRODQUAL =~   C_REP3   3.481 -0.051  -0.037   -0.066   -0.066
## 215     PROF  ~    AFCOM   3.457  0.067   0.083    0.083    0.083
## 216     PROF ~~    AFCOM   3.457  0.060   0.069    0.069    0.069
## 217     Im14 ~~      Im6   3.437  0.026   0.026    0.139    0.139
## 218   COM_A1 ~~   COM_A3   3.376 -0.096  -0.096   -0.117   -0.117
## 219   COM_A4 ~~    C_CR4   3.372  0.118   0.118    0.108    0.108
## 220     Im16 ~~    SAT_1   3.331 -0.049  -0.049   -0.121   -0.121
## 221      SAT  ~    ATMOS   3.317  0.068   0.098    0.098    0.098
## 222      Im2 ~~    SAT_2   3.313  0.034   0.034    0.104    0.104
## 223     Im10 ~~    C_CR1   3.270  0.043   0.043    0.124    0.124
## 224      COI  ~     PROF   3.265 -0.271  -0.148   -0.148   -0.148
## 225      Im2 ~~     Im17   3.241  0.032   0.032    0.181    0.181
## 226     Im20 ~~   C_REP2   3.189  0.026   0.026    0.148    0.148
## 227      Im3 ~~     Im17   3.176  0.028   0.028    0.194    0.194
## 228   COM_A3 ~~   C_REP3   3.161 -0.032  -0.032   -0.095   -0.095
## 229      COI =~   C_REP2   3.155 -0.019  -0.033   -0.052   -0.052
## 230     Im13 ~~   C_REP2   3.105  0.021   0.021    0.155    0.155
## 231     Im18 ~~      Im6   3.102  0.046   0.046    0.093    0.093
## 232     Im13 ~~   C_REP1   3.080 -0.028  -0.028   -0.104   -0.104
## 233   FRENCH  ~      COI   3.046 -0.044  -0.077   -0.077   -0.077
## 234   FRENCH =~     Im11   3.004  0.082   0.080    0.070    0.070
## 235      Im5 ~~   C_REP1   2.994  0.033   0.033    0.087    0.087
## 236     PROF =~     Im13   2.985  0.108   0.100    0.082    0.082
## 237    AFCOM =~     Im16   2.981 -0.068  -0.077   -0.064   -0.064
## 238     FOOD =~    C_CR4   2.973  0.130   0.107    0.053    0.053
## 239     Im22 ~~   COM_A1   2.964 -0.067  -0.067   -0.107   -0.107
## 240     Im20 ~~     Im22   2.926  0.135   0.135    0.231    0.231
## 241    SAT_1 ~~    C_CR4   2.910  0.068   0.068    0.112    0.112
## 242    ATMOS =~   C_REP2   2.903 -0.029  -0.036   -0.058   -0.058
## 243     Im16 ~~   C_REP3   2.902 -0.026  -0.026   -0.091   -0.091
## 244      Im3 ~~      Im2   2.887  0.026   0.026    0.097    0.097
## 245     Im17 ~~   C_REP1   2.875 -0.023  -0.023   -0.168   -0.168
## 246    BRAND =~    SAT_2   2.836  0.051   0.062    0.062    0.062
## 247     Im18 ~~   COM_A1   2.835 -0.056  -0.056   -0.090   -0.090
## 248     Im22 ~~     Im12   2.826 -0.049  -0.049   -0.122   -0.122
## 249    AFCOM =~    C_CR4   2.820  0.104   0.119    0.059    0.059
## 250     Im22 ~~    SAT_1   2.816  0.045   0.045    0.122    0.122
## 251    ATMOS =~    C_CR1   2.795 -0.085  -0.107   -0.054   -0.054
## 252   COM_A4 ~~   C_REP1   2.781  0.037   0.037    0.093    0.093
## 253     Im10 ~~     Im11   2.768  0.029   0.029    0.096    0.096
## 254      Im2 ~~   C_REP2   2.762 -0.016  -0.016   -0.128   -0.128
## 255      COI =~     Im16   2.755 -0.041  -0.069   -0.057   -0.057
## 256     Im14 ~~    SAT_2   2.753  0.020   0.020    0.129    0.129
## 257      SAT =~   COM_A1   2.742  0.088   0.077    0.054    0.054
## 258     Im11 ~~    SAT_1   2.737  0.045   0.045    0.098    0.098
## 259   COM_A1 ~~   C_REP2   2.709  0.024   0.024    0.128    0.128
## 260      Im7 ~~   C_REP2   2.704 -0.018  -0.018   -0.232   -0.232
## 261     Im13 ~~   COM_A2   2.663 -0.055  -0.055   -0.101   -0.101
## 262     Im13 ~~    SAT_2   2.660  0.037   0.037    0.105    0.105
## 263      Im3 ~~   COM_A4   2.657  0.043   0.043    0.099    0.099
## 264     Im12 ~~      Im6   2.654 -0.038  -0.038   -0.100   -0.100
## 265      Im5 ~~      Im1   2.639  0.040   0.040    0.164    0.164
## 266   COM_A3 ~~    SAT_1   2.580  0.050   0.050    0.103    0.103
## 267      Im5 ~~      Im7   2.574  0.046   0.046    0.148    0.148
## 268     Im12 ~~    SAT_3   2.549  0.047   0.047    0.098    0.098
## 269    AFCOM =~    SAT_1   2.547  0.045   0.051    0.050    0.050
## 270   CHOICE =~     Im14   2.541  0.027   0.035    0.040    0.040
## 271   CHOICE =~     Im10   2.541 -0.027  -0.035   -0.039   -0.039
## 272     FOOD =~    SAT_2   2.535  0.067   0.055    0.054    0.054
## 273      COI =~     Im11   2.529  0.042   0.070    0.061    0.061
## 274   FRENCH =~      Im1   2.523 -0.055  -0.054   -0.041   -0.041
## 275      SAT =~      Im4   2.513 -0.055  -0.048   -0.035   -0.035
## 276      Im1 ~~     Im17   2.506 -0.029  -0.029   -0.334   -0.334
## 277      SAT =~      Im5   2.505  0.084   0.074    0.056    0.056
## 278       RI =~     Im16   2.491 -0.120  -0.072   -0.059   -0.059
## 279     Im20 ~~   COM_A2   2.487 -0.066  -0.066   -0.093   -0.093
## 280      SAT ~~      COI   2.484  0.180   0.174    0.174    0.174
## 281      Im3 ~~     Im11   2.477  0.036   0.036    0.086    0.086
## 282      Im5 ~~     Im14   2.466  0.026   0.026    0.108    0.108
## 283     Im14 ~~      Im7   2.465 -0.023  -0.023   -0.239   -0.239
## 284      COI  ~      Im8   2.456 -0.108  -0.064   -0.068   -0.064
## 285   FRENCH =~    C_CR4   2.455  0.100   0.098    0.049    0.049
## 286     Im21 ~~    C_CR4   2.455  0.087   0.087    0.087    0.087
## 287      COI =~      Im2   2.430  0.027   0.045    0.035    0.035
## 288 PRODQUAL =~    SAT_2   2.425  0.081   0.058    0.058    0.058
## 289      Im4 ~~     Im22   2.405 -0.034  -0.034   -0.141   -0.141
## 290   COM_A2 ~~    SAT_2   2.367 -0.047  -0.047   -0.091   -0.091
## 291    AFCOM =~      Im2   2.359  0.042   0.047    0.037    0.037
## 292      Im3 ~~    C_CR1   2.345  0.048   0.048    0.099    0.099
## 293      Im5 ~~   COM_A2   2.339  0.062   0.062    0.080    0.080
## 294      Im4 ~~      Im1   2.328  0.022   0.022    0.241    0.241
## 295     FOOD =~      Im1   2.315 -0.066  -0.054   -0.041   -0.041
## 296      Im2 ~~     Im16   2.269  0.036   0.036    0.083    0.083
## 297     Im12 ~~     Im16   2.252  0.042   0.042    0.097    0.097
## 298     Im11 ~~   C_REP2   2.249 -0.022  -0.022   -0.110   -0.110
## 299 PRODQUAL  ~       RI   2.242 -0.135  -0.113   -0.113   -0.113
## 300      Im3 ~~     Im20   2.242 -0.034  -0.034   -0.091   -0.091
## 301   CHOICE =~    C_CR4   2.241  0.071   0.092    0.046    0.046
## 302      SAT  ~      Im9   2.193  0.038   0.043    0.058    0.043
## 303    ATMOS =~     Im13   2.191  0.054   0.068    0.056    0.056
## 304      SAT =~     Im20   2.163 -0.082  -0.072   -0.048   -0.048
## 305     Im20 ~~      Im1   2.156 -0.037  -0.037   -0.167   -0.167
## 306     PROF =~      Im4   2.126 -0.074  -0.068   -0.050   -0.050
## 307     Im19 ~~   COM_A1   2.106  0.046   0.046    0.088    0.088
## 308     FOOD =~   C_REP2   2.105 -0.030  -0.025   -0.039   -0.039
## 309      Im2 ~~   C_REP1   2.104  0.019   0.019    0.076    0.076
## 310   COM_A2 ~~   COM_A4   2.092 -0.092  -0.092   -0.113   -0.113
## 311     Im22 ~~      Im2   2.088 -0.036  -0.036   -0.089   -0.089
## 312     Im16 ~~    C_CR4   2.077 -0.076  -0.076   -0.082   -0.082
## 313   COM_A1 ~~    C_CR3   2.064  0.083   0.083    0.083    0.083
## 314     PROF  ~      Im8   2.061  0.042   0.046    0.048    0.046
## 315   C_REP3 ~~    C_CR3   2.044 -0.033  -0.033   -0.080   -0.080
## 316     Im10 ~~     Im12   2.039  0.019   0.019    0.102    0.102
## 317     Im22 ~~     Im13   2.037 -0.044  -0.044   -0.099   -0.099
## 318     Im11 ~~      Im2   2.033  0.036   0.036    0.072    0.072
## 319     DECO =~     Im12   2.017 -0.050  -0.062   -0.054   -0.054
## 320   FRENCH =~      Im5   2.012  0.065   0.063    0.048    0.048
## 321   CHOICE =~     Im22   2.008  0.057   0.074    0.048    0.048
## 322      Im2 ~~    C_CR1   2.006  0.049   0.049    0.085    0.085
## 323 PRODQUAL ~~      COI   2.003  0.114   0.104    0.104    0.104
## 324     Im18 ~~   C_REP1   1.975  0.023   0.023    0.074    0.074
## 325    BRAND =~   C_REP1   1.974  0.027   0.032    0.044    0.044
## 326     Im14 ~~      Im2   1.962  0.016   0.016    0.101    0.101
## 327      Im5 ~~    SAT_2   1.955  0.038   0.038    0.076    0.076
## 328   CHOICE =~     Im21   1.936  0.053   0.069    0.050    0.050
## 329 PRODQUAL =~     Im16   1.928 -0.119  -0.086   -0.071   -0.071
## 330      Im7 ~~   COM_A1   1.921 -0.043  -0.043   -0.136   -0.136
## 331      Im3 ~~     Im14   1.918 -0.014  -0.014   -0.109   -0.109
## 332     Im21 ~~    C_CR3   1.915 -0.078  -0.078   -0.079   -0.079
## 333 PRODQUAL =~      Im4   1.915 -0.064  -0.046   -0.034   -0.034
## 334   COM_A2 ~~    SAT_3   1.882  0.058   0.058    0.075    0.075
## 335     Im14 ~~   C_REP3   1.859  0.009   0.009    0.097    0.097
## 336     Im14 ~~     Im12   1.858 -0.018  -0.018   -0.118   -0.118
## 337    SAT_1 ~~    C_CR1   1.843 -0.052  -0.052   -0.096   -0.096
## 338    SAT_2 ~~    C_CR3   1.838  0.056   0.056    0.084    0.084
## 339       RI =~    SAT_1   1.836 -0.086  -0.052   -0.051   -0.051
## 340       RI =~     Im11   1.827  0.105   0.063    0.055    0.055
## 341     Im14 ~~   COM_A3   1.826  0.026   0.026    0.100    0.100
## 342   COM_A1 ~~    SAT_2   1.813  0.039   0.039    0.077    0.077
## 343       RI =~     Im10   1.807 -0.047  -0.028   -0.032   -0.032
## 344     Im22 ~~    SAT_2   1.794 -0.037  -0.037   -0.089   -0.089
## 345     Im13 ~~    SAT_3   1.781 -0.042  -0.042   -0.078   -0.078
## 346      COI =~      Im1   1.763 -0.023  -0.038   -0.029   -0.029
## 347    ATMOS =~   COM_A2   1.735 -0.063  -0.079   -0.049   -0.049
## 348      Im5 ~~     Im16   1.734 -0.046  -0.046   -0.068   -0.068
## 349    ATMOS ~~      COI   1.717  0.232   0.121    0.121    0.121
## 350      COI =~     Im13   1.710 -0.029  -0.049   -0.041   -0.041
## 351    BRAND =~      Im3   1.692  0.035   0.043    0.032    0.032
## 352      SAT =~     Im18   1.689 -0.069  -0.061   -0.043   -0.043
## 353     FOOD =~      Im2   1.646  0.050   0.041    0.032    0.032
## 354     FOOD ~~      SAT   1.640  0.030   0.054    0.054    0.054
## 355      Im7 ~~    SAT_3   1.637  0.039   0.039    0.123    0.123
## 356 PRODQUAL =~      Im7   1.627  0.090   0.065    0.053    0.053
## 357 PRODQUAL =~      Im6   1.627 -0.076  -0.054   -0.045   -0.045
## 358    AFCOM =~      Im7   1.623 -0.054  -0.062   -0.051   -0.051
## 359   FRENCH =~      Im2   1.618  0.039   0.039    0.030    0.030
## 360     Im20 ~~   COM_A1   1.616 -0.050  -0.050   -0.072   -0.072
## 361      Im3 ~~   COM_A3   1.609 -0.033  -0.033   -0.075   -0.075
## 362   FRENCH =~   COM_A2   1.609 -0.066  -0.065   -0.041   -0.041
## 363   CHOICE =~     Im16   1.590  0.063   0.083    0.069    0.069
## 364   CHOICE =~     Im19   1.590 -0.066  -0.086   -0.076   -0.076
## 365      Im3 ~~     Im12   1.578 -0.022  -0.022   -0.084   -0.084
## 366    ATMOS  ~      SAT   1.575  0.108   0.075    0.075    0.075
## 367    ATMOS ~~      SAT   1.575  0.049   0.058    0.058    0.058
## 368   C_REP3 ~~    C_CR4   1.552  0.029   0.029    0.068    0.068
## 369     Im12 ~~   COM_A4   1.535 -0.042  -0.042   -0.081   -0.081
## 370     PROF =~      Im7   1.532 -0.079  -0.073   -0.060   -0.060
## 371     Im20 ~~   COM_A3   1.528 -0.054  -0.054   -0.072   -0.072
## 372       RI =~      Im7   1.511 -0.077  -0.046   -0.038   -0.038
## 373      SAT =~     Im17   1.505  0.056   0.049    0.039    0.039
## 374   FRENCH ~~      COI   1.501 -0.076  -0.051   -0.051   -0.051
## 375 PRODQUAL =~     Im22   1.487 -0.093  -0.067   -0.044   -0.044
## 376     Im12 ~~     Im13   1.487  0.088   0.088    0.259    0.259
## 377    ATMOS =~    SAT_2   1.484  0.035   0.044    0.043    0.043
## 378     Im21 ~~     Im18   1.482 -0.040  -0.040   -0.065   -0.065
## 379    ATMOS =~   COM_A3   1.482  0.060   0.076    0.047    0.047
## 380      SAT =~     Im19   1.460 -0.093  -0.082   -0.072   -0.072
## 381     PROF =~      Im5   1.459  0.083   0.077    0.057    0.057
## 382     Im22 ~~     Im19   1.456 -0.038  -0.038   -0.086   -0.086
## 383 PRODQUAL =~   C_REP2   1.451  0.034   0.024    0.039    0.039
## 384      Im2 ~~     Im18   1.442 -0.026  -0.026   -0.064   -0.064
## 385      Im3 ~~     Im18   1.438 -0.023  -0.023   -0.069   -0.069
## 386     Im19 ~~     Im17   1.423  0.028   0.028    0.146    0.146
## 387     Im20 ~~    SAT_2   1.417  0.034   0.034    0.072    0.072
## 388     Im13 ~~     Im18   1.406 -0.032  -0.032   -0.071   -0.071
## 389     FOOD =~     Im16   1.383 -0.080  -0.065   -0.054   -0.054
## 390      Im7 ~~   COM_A2   1.379 -0.038  -0.038   -0.120   -0.120
## 391     Im12 ~~     Im17   1.379 -0.025  -0.025   -0.143   -0.143
## 392      Im2 ~~   COM_A3   1.371  0.033   0.033    0.064    0.064
## 393     Im12 ~~   COM_A3   1.368 -0.039  -0.039   -0.075   -0.075
## 394    ATMOS =~      Im3   1.353  0.030   0.037    0.028    0.028
## 395    BRAND =~     Im16   1.347 -0.062  -0.075   -0.062   -0.062
## 396    ATMOS =~     Im18   1.347  0.052   0.065    0.047    0.047
## 397    ATMOS =~     Im17   1.347 -0.052  -0.066   -0.052   -0.052
## 398     Im10 ~~    C_CR4   1.345 -0.029  -0.029   -0.073   -0.073
## 399       RI =~      Im4   1.337 -0.051  -0.031   -0.023   -0.023
## 400     Im14 ~~     Im17   1.336  0.014   0.014    0.161    0.161
## 401     Im14 ~~    C_CR4   1.329  0.028   0.028    0.087    0.087
## 402      COI =~      Im4   1.325 -0.017  -0.029   -0.021   -0.021
## 403     Im10 ~~     Im17   1.317 -0.014  -0.014   -0.132   -0.132
## 404     Im17 ~~   COM_A1   1.311  0.031   0.031    0.115    0.115
## 405      Im2 ~~    SAT_1   1.302 -0.021  -0.021   -0.072   -0.072
## 406   COM_A2 ~~    C_CR1   1.300  0.065   0.065    0.071    0.071
## 407 PRODQUAL =~     Im17   1.290  0.103   0.074    0.059    0.059
## 408 PRODQUAL =~     Im18   1.290 -0.102  -0.073   -0.052   -0.052
## 409   FRENCH =~    SAT_3   1.289  0.052   0.051    0.045    0.045
## 410      Im2 ~~   C_REP3   1.282  0.012   0.012    0.059    0.059
## 411      Im1 ~~   COM_A4   1.275 -0.032  -0.032   -0.126   -0.126
## 412     Im12 ~~    C_CR1   1.270 -0.045  -0.045   -0.079   -0.079
## 413     Im18 ~~      Im7   1.266 -0.028  -0.028   -0.110   -0.110
## 414      Im4 ~~      Im2   1.241 -0.016  -0.016   -0.087   -0.087
## 415      Im3 ~~     Im10   1.223  0.011   0.011    0.073    0.073
## 416    ATMOS =~    C_CR3   1.217 -0.060  -0.075   -0.036   -0.036
## 417      SAT =~     Im11   1.212  0.061   0.054    0.047    0.047
## 418     Im21 ~~    SAT_3   1.204  0.043   0.043    0.057    0.057
## 419     Im16 ~~      Im7   1.197 -0.032  -0.032   -0.113   -0.113
## 420 PRODQUAL =~   COM_A2   1.192 -0.077  -0.055   -0.034   -0.034
## 421   C_REP1 ~~    C_CR3   1.189  0.031   0.031    0.062    0.062
## 422      SAT =~     Im14   1.184  0.028   0.025    0.028    0.028
## 423     Im10 ~~   COM_A4   1.177 -0.022  -0.022   -0.069   -0.069
## 424     Im10 ~~    SAT_2   1.174 -0.014  -0.014   -0.071   -0.071
## 425     Im11 ~~      Im7   1.165  0.032   0.032    0.100    0.100
## 426      Im5 ~~     Im19   1.164 -0.033  -0.033   -0.062   -0.062
## 427   COM_A4 ~~    SAT_3   1.160 -0.048  -0.048   -0.059   -0.059
## 428     Im12 ~~   C_REP1   1.159 -0.016  -0.016   -0.067   -0.067
## 429     Im20 ~~     Im18   1.147  0.035   0.035    0.061    0.061
## 430 PRODQUAL =~     Im20   1.141  0.080   0.057    0.038    0.038
## 431     Im12 ~~    C_CR3   1.140  0.046   0.046    0.072    0.072
## 432      Im4 ~~      Im7   1.131 -0.018  -0.018   -0.155   -0.155
## 433   FRENCH =~    SAT_1   1.130  0.035   0.035    0.034    0.034
## 434 PRODQUAL =~   COM_A3   1.117  0.077   0.056    0.034    0.034
## 435     Im14 ~~     Im13   1.110  0.015   0.015    0.087    0.087
## 436    AFCOM =~    C_CR1   1.103 -0.063  -0.072   -0.036   -0.036
## 437   FRENCH =~   COM_A1   1.099 -0.052  -0.051   -0.035   -0.035
## 438   COM_A1 ~~    C_CR1   1.089 -0.057  -0.057   -0.063   -0.063
## 439     Im12 ~~    SAT_2   1.087 -0.022  -0.022   -0.070   -0.070
## 440     Im17 ~~   COM_A4   1.079 -0.032  -0.032   -0.109   -0.109
## 441     DECO =~     Im13   1.077  0.039   0.048    0.039    0.039
## 442   COM_A4 ~~   C_REP3   1.063 -0.019  -0.019   -0.056   -0.056
## 443     Im13 ~~     Im19   1.052  0.027   0.027    0.071    0.071
## 444     Im21 ~~     Im11   1.051 -0.039  -0.039   -0.052   -0.052
## 445    AFCOM =~    SAT_3   1.047  0.040   0.046    0.041    0.041
## 446     Im12 ~~    C_CR4   1.046  0.043   0.043    0.067    0.067
## 447      Im7 ~~   COM_A4   1.043  0.035   0.035    0.106    0.106
## 448      Im4 ~~     Im12   1.040  0.017   0.017    0.093    0.093
## 449      Im6 ~~      Im7   1.038  0.377   0.377    1.511    1.511
## 450   FRENCH ~~    AFCOM   1.037 -0.074  -0.080   -0.080   -0.080
## 451   FRENCH  ~    AFCOM   1.037 -0.082  -0.096   -0.096   -0.096
## 452      Im6 ~~   COM_A1   1.037  0.033   0.033    0.054    0.054
## 453      COI  ~     DECO   1.023 -0.077  -0.057   -0.057   -0.057
## 454     Im19 ~~    SAT_3   1.022 -0.032  -0.032   -0.061   -0.061
## 455   COM_A1 ~~   C_REP3   1.022  0.017   0.017    0.053    0.053
## 456    AFCOM  ~     DECO   1.018  0.048   0.052    0.052    0.052
## 457      Im4 ~~   COM_A4   1.008 -0.025  -0.025   -0.082   -0.082
## 458      SAT =~      Im1   0.995 -0.055  -0.049   -0.037   -0.037
## 459    AFCOM  ~      Im8   0.987  0.042   0.037    0.039    0.037
## 460     PROF =~   COM_A1   0.986  0.053   0.048    0.034    0.034
## 461      Im6 ~~   C_REP2   0.985  0.012   0.012    0.076    0.076
## 462     Im13 ~~      Im6   0.984  0.025   0.025    0.059    0.059
## 463   FRENCH =~   COM_A4   0.976  0.055   0.054    0.031    0.031
## 464    BRAND =~     Im10   0.972 -0.019  -0.023   -0.026   -0.026
## 465    BRAND =~     Im14   0.972  0.019   0.023    0.026    0.026
## 466   CHOICE =~    C_CR1   0.962 -0.044  -0.057   -0.029   -0.029
## 467   COM_A4 ~~    C_CR3   0.959 -0.064  -0.064   -0.059   -0.059
## 468   COM_A3 ~~    SAT_2   0.957  0.031   0.031    0.057    0.057
## 469     Im17 ~~   COM_A3   0.954  0.029   0.029    0.100    0.100
## 470    BRAND =~   COM_A4   0.951 -0.042  -0.051   -0.029   -0.029
## 471      Im3 ~~    SAT_1   0.947  0.016   0.016    0.066    0.066
## 472      Im1 ~~     Im18   0.942  0.021   0.021    0.104    0.104
## 473      COI =~   COM_A1   0.941 -0.029  -0.048   -0.034   -0.034
## 474     Im19 ~~     Im18   0.940 -0.026  -0.026   -0.059   -0.059
## 475      Im1 ~~   COM_A2   0.939  0.026   0.026    0.107    0.107
## 476     Im18 ~~    SAT_1   0.933 -0.022  -0.022   -0.060   -0.060
## 477      Im1 ~~   COM_A1   0.914  0.024   0.024    0.102    0.102
## 478     Im22 ~~     Im18   0.914  0.031   0.031    0.059    0.059
## 479      Im1 ~~   C_REP2   0.913  0.009   0.009    0.148    0.148
## 480     Im11 ~~     Im18   0.904  0.031   0.031    0.048    0.048
## 481    BRAND =~      Im1   0.884 -0.041  -0.050   -0.037   -0.037
## 482    AFCOM =~     Im21   0.883  0.045   0.051    0.037    0.037
## 483     Im17 ~~   C_REP2   0.882  0.009   0.009    0.136    0.136
## 484   FRENCH =~    C_CR3   0.881 -0.061  -0.060   -0.028   -0.028
## 485     Im12 ~~    SAT_1   0.880 -0.019  -0.019   -0.069   -0.069
## 486   CHOICE =~   COM_A1   0.870  0.032   0.042    0.029    0.029
## 487    ATMOS =~      Im2   0.868 -0.030  -0.038   -0.029   -0.029
## 488      SAT =~      Im2   0.867  0.046   0.041    0.032    0.032
## 489      Im6 ~~    SAT_1   0.860  0.021   0.021    0.057    0.057
## 490   FRENCH =~     Im13   0.859 -0.039  -0.038   -0.031   -0.031
## 491     Im13 ~~   COM_A4   0.859  0.033   0.033    0.058    0.058
## 492     Im18 ~~   C_REP3   0.853 -0.012  -0.012   -0.048   -0.048
## 493      Im4 ~~    C_CR3   0.847  0.030   0.030    0.077    0.077
## 494    AFCOM =~      Im1   0.843 -0.025  -0.029   -0.022   -0.022
## 495    AFCOM =~      Im4   0.840 -0.021  -0.025   -0.018   -0.018
## 496     Im22 ~~      Im6   0.839  0.028   0.028    0.056    0.056
## 497      Im5 ~~      Im2   0.838 -0.023  -0.023   -0.046   -0.046
## 498      Im9  ~      COI   0.833  0.031   0.052    0.038    0.038
## 499 PRODQUAL =~    SAT_1   0.833 -0.047  -0.034   -0.033   -0.033
## 500     Im12 ~~   COM_A2   0.831  0.029   0.029    0.059    0.059
## 501     Im20 ~~     Im19   0.831  0.029   0.029    0.059    0.059
## 502    BRAND =~     Im11   0.822 -0.041  -0.050   -0.043   -0.043
## 503     Im20 ~~      Im7   0.821  0.027   0.027    0.095    0.095
## 504      Im1 ~~   COM_A3   0.819 -0.025  -0.025   -0.098   -0.098
## 505     Im18 ~~   COM_A2   0.814  0.032   0.032    0.050    0.050
## 506      Im4 ~~      Im5   0.814  0.033   0.033    0.113    0.113
## 507     Im22 ~~   COM_A3   0.802  0.038   0.038    0.057    0.057
## 508      Im5 ~~     Im11   0.799  0.034   0.034    0.043    0.043
## 509     FOOD =~     Im20   0.793 -0.051  -0.042   -0.028   -0.028
## 510      COI =~   C_REP3   0.792 -0.010  -0.016   -0.029   -0.029
## 511     PROF =~     Im18   0.791 -0.080  -0.074   -0.052   -0.052
## 512     PROF =~     Im17   0.791  0.080   0.074    0.059    0.059
## 513      Im7 ~~   COM_A3   0.789  0.030   0.030    0.089    0.089
## 514     Im16 ~~    C_CR1   0.782  0.044   0.044    0.055    0.055
## 515     Im20 ~~    SAT_3   0.782  0.035   0.035    0.049    0.049
## 516      Im6 ~~    C_CR4   0.776 -0.040  -0.040   -0.048   -0.048
## 517     Im13 ~~      Im7   0.773 -0.022  -0.022   -0.098   -0.098
## 518     Im14 ~~     Im21   0.772  0.015   0.015    0.064    0.064
## 519      Im3 ~~     Im19   0.772  0.017   0.017    0.058    0.058
## 520    BRAND =~   COM_A2   0.766 -0.035  -0.043   -0.027   -0.027
## 521    SAT_3 ~~   C_REP3   0.758  0.014   0.014    0.045    0.045
## 522      Im5 ~~   C_REP2   0.755 -0.012  -0.012   -0.064   -0.064
## 523      Im5 ~~    C_CR4   0.748  0.047   0.047    0.046    0.046
## 524     PROF =~     Im22   0.747  0.056   0.051    0.034    0.034
## 525    AFCOM =~      Im6   0.745  0.032   0.037    0.031    0.031
## 526      COI =~      Im5   0.743  0.022   0.037    0.028    0.028
## 527     Im11 ~~   COM_A3   0.735  0.037   0.037    0.044    0.044
## 528    BRAND =~      Im2   0.731  0.033   0.040    0.031    0.031
## 529     PROF =~     Im11   0.723  0.054   0.049    0.043    0.043
## 530       RI =~     Im13   0.722  0.057   0.034    0.028    0.028
## 531     Im22 ~~      Im7   0.721  0.026   0.026    0.098    0.098
## 532 PRODQUAL =~     Im19   0.712  0.072   0.051    0.045    0.045
## 533      COI =~      Im3   0.712  0.013   0.022    0.017    0.017
## 534   COM_A3 ~~    SAT_3   0.702 -0.037  -0.037   -0.045   -0.045
## 535      COI  ~      Im9   0.700 -0.045  -0.027   -0.036   -0.027
## 536     Im10 ~~   C_REP3   0.700 -0.006  -0.006   -0.050   -0.050
## 537     Im11 ~~    C_CR4   0.696  0.047   0.047    0.044    0.044
## 538       RI  ~   CHOICE   0.694 -0.020  -0.044   -0.044   -0.044
## 539    SAT_3 ~~    C_CR1   0.689  0.045   0.045    0.049    0.049
## 540      SAT =~     Im21   0.686  0.045   0.040    0.029    0.029
## 541     Im11 ~~   COM_A2   0.683  0.034   0.034    0.043    0.043
## 542     Im21 ~~   COM_A1   0.681  0.032   0.032    0.044    0.044
## 543     Im12 ~~      Im2   0.678 -0.016  -0.016   -0.051   -0.051
## 544     Im14 ~~     Im18   0.675 -0.012  -0.012   -0.060   -0.060
## 545     Im13 ~~    C_CR3   0.675 -0.038  -0.038   -0.053   -0.053
## 546     Im19 ~~    SAT_1   0.673 -0.019  -0.019   -0.062   -0.062
## 547   CHOICE  ~      Im8   0.672 -0.035  -0.027   -0.028   -0.027
## 548     Im22 ~~    C_CR1   0.664 -0.043  -0.043   -0.057   -0.057
## 549      SAT =~    C_CR3   0.662 -0.063  -0.056   -0.027   -0.027
## 550   COM_A4 ~~   C_REP2   0.661 -0.013  -0.013   -0.067   -0.067
## 551     DECO =~    SAT_2   0.661  0.024   0.030    0.030    0.030
## 552     Im10 ~~     Im18   0.651  0.012   0.012    0.049    0.049
## 553   CHOICE =~    SAT_2   0.648 -0.026  -0.033   -0.033   -0.033
## 554     Im14 ~~    SAT_1   0.648 -0.010  -0.010   -0.069   -0.069
## 555     Im16 ~~   COM_A4   0.646 -0.033  -0.033   -0.046   -0.046
## 556      Im7 ~~    C_CR4   0.638  0.034   0.034    0.081    0.081
## 557     Im10 ~~   COM_A1   0.633 -0.014  -0.014   -0.048   -0.048
## 558      SAT ~~       RI   0.629  0.029   0.086    0.086    0.086
## 559     Im21 ~~   COM_A4   0.627 -0.035  -0.035   -0.044   -0.044
## 560     PROF =~      Im3   0.627  0.039   0.036    0.027    0.027
## 561      SAT =~     Im16   0.627 -0.061  -0.054   -0.044   -0.044
## 562      Im6 ~~   COM_A3   0.626 -0.028  -0.028   -0.043   -0.043
## 563     Im21 ~~   C_REP1   0.623 -0.015  -0.015   -0.042   -0.042
## 564      Im4 ~~   COM_A2   0.621 -0.019  -0.019   -0.064   -0.064
## 565    ATMOS  ~      Im8   0.621  0.036   0.028    0.030    0.028
## 566      SAT =~     Im22   0.619 -0.044  -0.038   -0.025   -0.025
## 567     Im22 ~~   COM_A4   0.618  0.034   0.034    0.051    0.051
## 568     Im22 ~~     Im17   0.617  0.021   0.021    0.093    0.093
## 569     Im19 ~~    SAT_2   0.615  0.019   0.019    0.053    0.053
## 570     Im10 ~~   COM_A3   0.615 -0.015  -0.015   -0.049   -0.049
## 571     Im22 ~~     Im16   0.612  0.028   0.028    0.050    0.050
## 572    SAT_3 ~~   C_REP2   0.608 -0.011  -0.011   -0.059   -0.059
## 573     Im16 ~~    SAT_3   0.601  0.029   0.029    0.042    0.042
## 574   COM_A1 ~~   C_REP1   0.600 -0.015  -0.015   -0.041   -0.041
## 575     Im10 ~~      Im2   0.597 -0.009  -0.009   -0.047   -0.047
## 576    SAT_1 ~~   C_REP1   0.595  0.011   0.011    0.048    0.048
## 577     Im22 ~~   COM_A2   0.593  0.032   0.032    0.049    0.049
## 578      Im4 ~~     Im16   0.572  0.016   0.016    0.062    0.062
## 579     FOOD ~~      COI   0.565 -0.036  -0.029   -0.029   -0.029
## 580   CHOICE =~     Im11   0.562 -0.029  -0.038   -0.033   -0.033
## 581      COI =~     Im21   0.561  0.020   0.034    0.025    0.025
## 582   COM_A2 ~~    C_CR4   0.561 -0.045  -0.045   -0.043   -0.043
## 583       RI =~      Im1   0.556 -0.040  -0.024   -0.018   -0.018
## 584   CHOICE =~    SAT_1   0.553  0.024   0.032    0.031    0.031
## 585     FOOD =~    SAT_3   0.552  0.042   0.034    0.030    0.030
## 586   CHOICE =~   C_REP2   0.551 -0.010  -0.013   -0.021   -0.021
## 587   CHOICE =~      Im3   0.549 -0.017  -0.022   -0.017   -0.017
## 588   COM_A4 ~~    SAT_2   0.547  0.024   0.024    0.045    0.045
## 589      Im4 ~~     Im10   0.545 -0.007  -0.007   -0.066   -0.066
## 590     PROF =~      Im6   0.544  0.040   0.037    0.031    0.031
## 591       RI =~     Im18   0.539 -0.050  -0.030   -0.021   -0.021
## 592    BRAND =~    SAT_3   0.538 -0.029  -0.035   -0.031   -0.031
## 593      Im6 ~~    SAT_3   0.532 -0.023  -0.023   -0.038   -0.038
## 594   COM_A2 ~~    C_CR3   0.531 -0.045  -0.045   -0.044   -0.044
## 595 PRODQUAL =~     Im10   0.530 -0.028  -0.020   -0.023   -0.023
## 596 PRODQUAL =~     Im14   0.530  0.029   0.021    0.024    0.024
## 597     Im21 ~~    SAT_2   0.529 -0.020  -0.020   -0.042   -0.042
## 598    ATMOS =~      Im1   0.528  0.026   0.033    0.025    0.025
## 599      SAT  ~ PRODQUAL   0.527  0.051   0.041    0.041    0.041
## 600   CHOICE ~~       RI   0.522 -0.018  -0.028   -0.028   -0.028
## 601      Im7 ~~    SAT_2   0.513 -0.016  -0.016   -0.075   -0.075
## 602    ATMOS =~     Im19   0.502 -0.031  -0.039   -0.035   -0.035
## 603     Im13 ~~   COM_A3   0.502 -0.025  -0.025   -0.043   -0.043
## 604     Im11 ~~   COM_A1   0.500 -0.028  -0.028   -0.036   -0.036
## 605     Im14 ~~     Im20   0.490 -0.012  -0.012   -0.054   -0.054
## 606      Im7 ~~    C_CR1   0.488 -0.029  -0.029   -0.077   -0.077
## 607   COM_A2 ~~   C_REP2   0.488 -0.011  -0.011   -0.057   -0.057
## 608      Im2 ~~   COM_A4   0.487  0.020   0.020    0.039    0.039
## 609      Im6 ~~   COM_A2   0.478  0.023   0.023    0.038    0.038
## 610     Im17 ~~   C_REP3   0.478  0.008   0.008    0.068    0.068
## 611      Im3 ~~   COM_A2   0.478 -0.017  -0.017   -0.041   -0.041
## 612     FOOD =~    C_CR3   0.476 -0.053  -0.043   -0.021   -0.021
## 613      COI =~   COM_A3   0.475 -0.022  -0.038   -0.023   -0.023
## 614   FRENCH =~    SAT_2   0.474  0.023   0.023    0.023    0.023
## 615      Im5 ~~     Im21   0.462 -0.025  -0.025   -0.034   -0.034
## 616     Im10 ~~    SAT_3   0.458  0.012   0.012    0.040    0.040
## 617     Im20 ~~   C_REP3   0.456 -0.011  -0.011   -0.037   -0.037
## 618     Im21 ~~     Im17   0.453  0.018   0.018    0.068    0.068
## 619      Im2 ~~   COM_A1   0.453 -0.017  -0.017   -0.036   -0.036
## 620   COM_A1 ~~    C_CR4   0.451 -0.038  -0.038   -0.037   -0.037
## 621   C_REP2 ~~    C_CR3   0.446  0.014   0.014    0.056    0.056
## 622     PROF ~~      COI   0.436 -0.040  -0.028   -0.028   -0.028
## 623     Im17 ~~      Im7   0.434 -0.015  -0.015   -0.129   -0.129
## 624       RI =~      Im6   0.434  0.042   0.025    0.021    0.021
## 625     DECO =~     Im11   0.433  0.026   0.033    0.028    0.028
## 626   FRENCH  ~       RI   0.433 -0.051  -0.031   -0.031   -0.031
## 627      Im3 ~~    C_CR4   0.430 -0.022  -0.022   -0.039   -0.039
## 628    ATMOS  ~      Im9   0.429  0.023   0.018    0.025    0.018
## 629      Im7 ~~   C_REP1   0.428  0.010   0.010    0.063    0.063
## 630     Im16 ~~   COM_A3   0.426  0.027   0.027    0.037    0.037
## 631      Im5 ~~     Im17   0.425  0.017   0.017    0.062    0.062
## 632     Im10 ~~     Im20   0.424  0.011   0.011    0.042    0.042
## 633     FOOD =~      Im3   0.422 -0.023  -0.019   -0.014   -0.014
## 634     PROF =~    C_CR3   0.422 -0.047  -0.043   -0.021   -0.021
## 635      Im4 ~~   C_REP3   0.417 -0.006  -0.006   -0.049   -0.049
## 636      Im5 ~~    C_CR3   0.414 -0.035  -0.035   -0.035   -0.035
## 637      Im7 ~~   C_REP3   0.411  0.008   0.008    0.061    0.061
## 638     FOOD =~   COM_A2   0.411 -0.038  -0.031   -0.019   -0.019
## 639      Im5 ~~     Im22   0.406  0.024   0.024    0.037    0.037
## 640      COI =~     Im12   0.404  0.013   0.022    0.020    0.020
## 641   CHOICE =~    C_CR3   0.403 -0.030  -0.040   -0.019   -0.019
## 642     Im10 ~~    C_CR3   0.397 -0.016  -0.016   -0.041   -0.041
## 643    SAT_1 ~~    C_CR3   0.397 -0.026  -0.026   -0.043   -0.043
## 644     FOOD =~     Im19   0.394 -0.042  -0.035   -0.031   -0.031
## 645      Im1 ~~    C_CR1   0.393 -0.022  -0.022   -0.075   -0.075
## 646   FRENCH ~~       RI   0.393 -0.012  -0.026   -0.026   -0.026
## 647      Im3 ~~      Im7   0.392 -0.011  -0.011   -0.066   -0.066
## 648     Im12 ~~   C_REP2   0.391  0.007   0.007    0.057    0.057
## 649    AFCOM =~     Im14   0.390  0.011   0.013    0.015    0.015
## 650      Im4 ~~    SAT_1   0.390 -0.010  -0.010   -0.058   -0.058
## 651     Im10 ~~    SAT_1   0.390  0.008   0.008    0.045    0.045
## 652      COI =~      Im7   0.389 -0.013  -0.022   -0.018   -0.018
## 653     Im20 ~~      Im2   0.386 -0.016  -0.016   -0.035   -0.035
## 654    ATMOS ~~       RI   0.382  0.035   0.056    0.056    0.056
## 655     Im10 ~~     Im19   0.379 -0.009  -0.009   -0.044   -0.044
## 656      Im5 ~~     Im10   0.378 -0.010  -0.010   -0.035   -0.035
## 657     Im16 ~~    C_CR3   0.377 -0.033  -0.033   -0.036   -0.036
## 658    BRAND =~     Im19   0.376  0.032   0.039    0.035    0.035
## 659     DECO =~    SAT_1   0.374 -0.019  -0.023   -0.023   -0.023
## 660   C_REP3 ~~    C_CR1   0.373  0.013   0.013    0.036    0.036
## 661   FRENCH =~   C_REP3   0.369 -0.011  -0.011   -0.020   -0.020
## 662     Im17 ~~    SAT_1   0.367  0.011   0.011    0.071    0.071
## 663      Im4 ~~     Im14   0.358  0.006   0.006    0.064    0.064
## 664      COI =~     Im14   0.356 -0.007  -0.012   -0.013   -0.013
## 665     Im19 ~~   COM_A2   0.355 -0.020  -0.020   -0.037   -0.037
## 666     Im19 ~~      Im7   0.353  0.015   0.015    0.070    0.070
## 667     DECO =~    SAT_3   0.351 -0.023  -0.028   -0.025   -0.025
## 668      SAT =~      Im6   0.347  0.026   0.023    0.019    0.019
## 669     Im14 ~~   COM_A4   0.346  0.011   0.011    0.045    0.045
## 670     Im17 ~~    SAT_3   0.346 -0.016  -0.016   -0.058   -0.058
## 671 PRODQUAL =~   COM_A1   0.335  0.038   0.028    0.019    0.019
## 672   FRENCH =~      Im3   0.333 -0.017  -0.016   -0.012   -0.012
## 673   CHOICE  ~      COI   0.329  0.018   0.023    0.023    0.023
## 674    AFCOM =~     Im13   0.323 -0.020  -0.022   -0.018   -0.018
## 675     Im16 ~~    SAT_2   0.323  0.015   0.015    0.034    0.034
## 676     Im18 ~~   C_REP2   0.320 -0.007  -0.007   -0.044   -0.044
## 677      Im5 ~~     Im20   0.320  0.021   0.021    0.030    0.030
## 678    BRAND =~    SAT_1   0.319 -0.017  -0.021   -0.020   -0.020
## 679   CHOICE =~     Im17   0.311  0.023   0.031    0.024    0.024
## 680   CHOICE =~     Im18   0.311 -0.023  -0.030   -0.022   -0.022
## 681 PRODQUAL  ~      COI   0.305  0.017   0.040    0.040    0.040
## 682     Im20 ~~     Im12   0.297  0.016   0.016    0.036    0.036
## 683   CHOICE =~      Im4   0.296 -0.013  -0.017   -0.012   -0.012
## 684       RI =~     Im20   0.295  0.046   0.027    0.018    0.018
## 685      Im4 ~~    SAT_2   0.291 -0.009  -0.009   -0.045   -0.045
## 686     Im11 ~~    SAT_2   0.291 -0.015  -0.015   -0.029   -0.029
## 687   CHOICE =~      Im6   0.287 -0.015  -0.020   -0.016   -0.016
## 688      Im2 ~~      Im7   0.286  0.011   0.011    0.052    0.052
## 689     Im21 ~~    C_CR1   0.276  0.028   0.028    0.032    0.032
## 690    AFCOM =~    C_CR3   0.274 -0.033  -0.038   -0.018   -0.018
## 691      COI =~      Im6   0.271 -0.011  -0.019   -0.016   -0.016
## 692      Im2 ~~     Im19   0.264 -0.011  -0.011   -0.032   -0.032
## 693       RI =~      Im2   0.263  0.027   0.016    0.013    0.013
## 694      SAT =~      Im3   0.261  0.017   0.015    0.012    0.012
## 695      Im1 ~~     Im16   0.259 -0.012  -0.012   -0.058   -0.058
## 696     FOOD =~   COM_A1   0.255 -0.028  -0.023   -0.016   -0.016
## 697     Im21 ~~     Im12   0.255  0.015   0.015    0.031    0.031
## 698     FOOD =~     Im21   0.254  0.028   0.023    0.017    0.017
## 699      Im4 ~~    C_CR4   0.254  0.016   0.016    0.041    0.041
## 700     Im17 ~~    C_CR1   0.254 -0.018  -0.018   -0.057   -0.057
## 701      Im1 ~~    SAT_3   0.252  0.013   0.013    0.053    0.053
## 702    SAT_2 ~~   C_REP3   0.251  0.006   0.006    0.028    0.028
## 703     FOOD ~~       RI   0.250  0.008   0.019    0.019    0.019
## 704       RI  ~     PROF   0.241 -0.023  -0.036   -0.036   -0.036
## 705       RI =~   COM_A3   0.241  0.047   0.028    0.017    0.017
## 706     Im17 ~~    C_CR4   0.240  0.019   0.019    0.051    0.051
## 707     Im20 ~~     Im11   0.237  0.019   0.019    0.026    0.026
## 708   C_REP2 ~~    C_CR1   0.236  0.010   0.010    0.043    0.043
## 709     Im17 ~~      Im6   0.236  0.011   0.011    0.048    0.048
## 710     Im21 ~~     Im16   0.232 -0.017  -0.017   -0.026   -0.026
## 711    SAT_3 ~~    C_CR4   0.231  0.027   0.027    0.026    0.026
## 712     Im17 ~~    SAT_2   0.230  0.009   0.009    0.052    0.052
## 713     Im21 ~~      Im7   0.230 -0.014  -0.014   -0.047   -0.047
## 714    ATMOS =~     Im16   0.225 -0.021  -0.027   -0.022   -0.022
## 715    AFCOM  ~      Im9   0.224  0.016   0.014    0.019    0.014
## 716     DECO =~   C_REP2   0.223 -0.007  -0.008   -0.013   -0.013
## 717   COM_A2 ~~   C_REP3   0.220 -0.008  -0.008   -0.025   -0.025
## 718     Im19 ~~   COM_A4   0.215 -0.017  -0.017   -0.030   -0.030
## 719     Im13 ~~   COM_A1   0.215  0.015   0.015    0.028    0.028
## 720     Im22 ~~    C_CR3   0.211  0.026   0.026    0.031    0.031
## 721      Im5 ~~    SAT_1   0.209 -0.012  -0.012   -0.027   -0.027
## 722      SAT =~     Im10   0.207 -0.012  -0.011   -0.012   -0.012
## 723     DECO =~      Im2   0.204  0.014   0.017    0.014    0.014
## 724     DECO =~      Im1   0.204 -0.016  -0.020   -0.015   -0.015
## 725    SAT_2 ~~    C_CR4   0.203  0.019   0.019    0.027    0.027
## 726       RI =~      Im3   0.203  0.020   0.012    0.009    0.009
## 727    AFCOM =~     Im10   0.203 -0.008  -0.010   -0.011   -0.011
## 728     Im21 ~~      Im2   0.202  0.011   0.011    0.024    0.024
## 729    AFCOM =~     Im18   0.198 -0.016  -0.018   -0.013   -0.013
## 730   COM_A2 ~~    SAT_1   0.196 -0.013  -0.013   -0.029   -0.029
## 731     Im16 ~~   C_REP1   0.195  0.008   0.008    0.024    0.024
## 732     Im21 ~~      Im1   0.195  0.011   0.011    0.047    0.047
## 733    ATMOS =~     Im10   0.194 -0.008  -0.010   -0.011   -0.011
## 734    ATMOS =~     Im14   0.194  0.008   0.010    0.012    0.012
## 735      Im2 ~~    C_CR4   0.192 -0.016  -0.016   -0.024   -0.024
## 736    C_CR1 ~~    C_CR3   0.189  0.116   0.116    0.097    0.097
## 737      Im1 ~~      Im6   0.188 -0.009  -0.009   -0.046   -0.046
## 738     Im21 ~~   COM_A3   0.188 -0.019  -0.019   -0.024   -0.024
## 739      Im5 ~~   COM_A4   0.187 -0.019  -0.019   -0.023   -0.023
## 740     Im14 ~~    C_CR3   0.184  0.011   0.011    0.034    0.034
## 741   COM_A3 ~~    C_CR3   0.182  0.027   0.027    0.025    0.025
## 742     Im14 ~~    SAT_3   0.181 -0.007  -0.007   -0.030   -0.030
## 743 PRODQUAL =~   COM_A4   0.178 -0.032  -0.023   -0.013   -0.013
## 744      Im3 ~~   COM_A1   0.176 -0.010  -0.010   -0.024   -0.024
## 745     Im11 ~~   COM_A4   0.175  0.018   0.018    0.022    0.022
## 746     Im14 ~~     Im11   0.174  0.007   0.007    0.029    0.029
## 747       RI  ~   FRENCH   0.174 -0.012  -0.019   -0.019   -0.019
## 748    AFCOM ~~       RI   0.174  0.045   0.097    0.097    0.097
## 749    BRAND ~~      COI   0.171  0.028   0.015    0.015    0.015
## 750     Im19 ~~   C_REP3   0.171  0.005   0.005    0.024    0.024
## 751      COI =~   COM_A4   0.170  0.014   0.023    0.013    0.013
## 752     Im17 ~~    C_CR3   0.169  0.016   0.016    0.044    0.044
## 753     Im19 ~~   COM_A3   0.169 -0.014  -0.014   -0.025   -0.025
## 754     Im12 ~~   C_REP3   0.168 -0.005  -0.005   -0.025   -0.025
## 755     Im20 ~~   C_REP1   0.166 -0.008  -0.008   -0.023   -0.023
## 756      Im3 ~~    SAT_2   0.164 -0.007  -0.007   -0.025   -0.025
## 757     Im10 ~~     Im21   0.164 -0.007  -0.007   -0.025   -0.025
## 758     Im17 ~~   COM_A2   0.162 -0.012  -0.012   -0.042   -0.042
## 759      Im6 ~~    C_CR1   0.162  0.017   0.017    0.024    0.024
## 760     Im14 ~~      Im1   0.159 -0.004  -0.004   -0.059   -0.059
## 761     Im21 ~~   COM_A2   0.159  0.016   0.016    0.022    0.022
## 762      Im4 ~~   COM_A1   0.159  0.009   0.009    0.031    0.031
## 763     Im20 ~~    C_CR1   0.154  0.021   0.021    0.025    0.025
## 764      COI  ~   CHOICE   0.153 -0.030  -0.023   -0.023   -0.023
## 765     Im11 ~~    C_CR1   0.152 -0.021  -0.021   -0.022   -0.022
## 766   CHOICE =~   COM_A4   0.151 -0.015  -0.020   -0.011   -0.011
## 767      Im8  ~      COI   0.150 -0.010  -0.017   -0.016   -0.016
## 768     Im14 ~~     Im22   0.150 -0.006  -0.006   -0.033   -0.033
## 769      Im5 ~~   COM_A1   0.150 -0.015  -0.015   -0.020   -0.020
## 770     Im14 ~~   C_REP1   0.142  0.003   0.003    0.027    0.027
## 771      Im4 ~~   C_REP2   0.140  0.003   0.003    0.042    0.042
## 772      SAT =~   C_REP3   0.139 -0.009  -0.008   -0.014   -0.014
## 773      Im3 ~~   C_REP1   0.139  0.004   0.004    0.021    0.021
## 774     Im12 ~~   COM_A1   0.137  0.011   0.011    0.023    0.023
## 775      Im7 ~~    C_CR3   0.136 -0.016  -0.016   -0.039   -0.039
## 776    BRAND =~   C_REP2   0.135  0.005   0.007    0.011    0.011
## 777     Im13 ~~    SAT_1   0.134 -0.008  -0.008   -0.026   -0.026
## 778      Im3 ~~   C_REP3   0.131  0.003   0.003    0.020    0.020
## 779     Im19 ~~      Im6   0.125 -0.009  -0.009   -0.021   -0.021
## 780     PROF =~    SAT_3   0.125 -0.025  -0.023   -0.020   -0.020
## 781      Im1 ~~      Im2   0.123  0.312   0.312    2.013    2.013
## 782     Im11 ~~     Im19   0.123 -0.011  -0.011   -0.020   -0.020
## 783   CHOICE ~~      SAT   0.123 -0.041  -0.046   -0.046   -0.046
## 784   CHOICE  ~      SAT   0.122 -0.089  -0.060   -0.060   -0.060
## 785   FRENCH =~     Im21   0.122 -0.017  -0.017   -0.012   -0.012
## 786     DECO  ~    AFCOM   0.121 -0.017  -0.015   -0.015   -0.015
## 787     DECO ~~    AFCOM   0.121 -0.015  -0.013   -0.013   -0.013
## 788     FOOD =~   C_REP3   0.120 -0.008  -0.006   -0.011   -0.011
## 789     Im10 ~~   C_REP2   0.118 -0.002  -0.002   -0.030   -0.030
## 790   COM_A3 ~~    C_CR1   0.117 -0.021  -0.021   -0.021   -0.021
## 791     PROF  ~      Im9   0.117 -0.008  -0.008   -0.011   -0.008
## 792     PROF  ~      COI   0.116  0.008   0.015    0.015    0.015
## 793     FOOD ~~    AFCOM   0.116  0.010   0.013    0.013    0.013
## 794      Im2 ~~      Im6   0.115 -0.007  -0.007   -0.018   -0.018
## 795      Im5 ~~    SAT_3   0.115 -0.013  -0.013   -0.017   -0.017
## 796      COI =~    SAT_3   0.115 -0.009  -0.015   -0.014   -0.014
## 797      Im4 ~~     Im20   0.112  0.007   0.007    0.028    0.028
## 798     Im16 ~~   COM_A1   0.112 -0.012  -0.012   -0.018   -0.018
## 799    ATMOS =~    SAT_1   0.112  0.009   0.012    0.012    0.012
## 800      Im6 ~~   C_REP1   0.111 -0.005  -0.005   -0.017   -0.017
## 801      Im6 ~~   C_REP3   0.111 -0.004  -0.004   -0.017   -0.017
## 802     FOOD =~      Im4   0.111 -0.012  -0.010   -0.007   -0.007
## 803   FRENCH =~     Im18   0.110  0.014   0.014    0.010    0.010
## 804   FRENCH =~     Im17   0.110 -0.014  -0.014   -0.011   -0.011
## 805      Im4 ~~     Im19   0.109 -0.006  -0.006   -0.031   -0.031
## 806     DECO  ~      Im9   0.106  0.010   0.008    0.011    0.008
## 807    SAT_2 ~~    C_CR1   0.103 -0.013  -0.013   -0.021   -0.021
## 808      Im1 ~~    C_CR3   0.103 -0.012  -0.012   -0.037   -0.037
## 809     FOOD =~    SAT_1   0.101 -0.013  -0.011   -0.011   -0.011
## 810    AFCOM =~     Im17   0.100  0.010   0.011    0.009    0.009
## 811     Im18 ~~    SAT_2   0.100  0.008   0.008    0.018    0.018
## 812     Im18 ~~    C_CR1   0.099  0.014   0.014    0.019    0.019
## 813     DECO ~~      COI   0.098 -0.022  -0.012   -0.012   -0.012
## 814     Im16 ~~     Im18   0.097 -0.010  -0.010   -0.017   -0.017
## 815      Im4 ~~   C_REP1   0.097 -0.003  -0.003   -0.024   -0.024
## 816     Im14 ~~   C_REP2   0.097 -0.002  -0.002   -0.033   -0.033
## 817    AFCOM =~     Im22   0.095  0.016   0.018    0.012    0.012
## 818     Im14 ~~   COM_A1   0.095  0.005   0.005    0.022    0.022
## 819       RI =~    C_CR1   0.094 -0.032  -0.019   -0.010   -0.010
## 820   COM_A2 ~~   C_REP1   0.093  0.006   0.006    0.017    0.017
## 821    AFCOM =~     Im19   0.092 -0.011  -0.012   -0.011   -0.011
## 822     Im20 ~~    C_CR3   0.091 -0.017  -0.017   -0.018   -0.018
## 823     DECO ~~       RI   0.091  0.007   0.011    0.011    0.011
## 824     Im21 ~~     Im13   0.089 -0.009  -0.009   -0.018   -0.018
## 825       RI =~     Im17   0.088  0.017   0.010    0.008    0.008
## 826   FRENCH =~     Im10   0.088 -0.012  -0.012   -0.013   -0.013
## 827   FRENCH =~     Im14   0.088  0.012   0.012    0.013    0.013
## 828 PRODQUAL ~~       RI   0.085  0.007   0.021    0.021    0.021
## 829     Im11 ~~     Im16   0.083 -0.010  -0.010   -0.015   -0.015
## 830     DECO =~   COM_A4   0.081  0.012   0.015    0.008    0.008
## 831     Im10 ~~   C_REP1   0.079  0.002   0.002    0.017    0.017
## 832     Im18 ~~    C_CR4   0.078 -0.013  -0.013   -0.016   -0.016
## 833     PROF ~~       RI   0.077 -0.005  -0.012   -0.012   -0.012
## 834     PROF =~     Im21   0.075  0.017   0.015    0.011    0.011
## 835     DECO  ~      COI   0.075 -0.008  -0.011   -0.011   -0.011
## 836      Im3 ~~    SAT_3   0.073 -0.006  -0.006   -0.015   -0.015
## 837      Im3 ~~   C_REP2   0.073 -0.002  -0.002   -0.023   -0.023
## 838    SAT_1 ~~   C_REP3   0.068  0.003   0.003    0.016    0.016
## 839     Im10 ~~      Im1   0.067 -0.003  -0.003   -0.032   -0.032
## 840      Im5 ~~     Im12   0.066  0.007   0.007    0.015    0.015
## 841     PROF  ~       RI   0.063  0.018   0.012    0.012    0.012
## 842      Im5 ~~     Im18   0.061  0.008   0.008    0.012    0.012
## 843    ATMOS  ~       RI   0.059  0.047   0.022    0.022    0.022
## 844 PRODQUAL =~     Im21   0.058  0.017   0.012    0.009    0.009
## 845       RI =~   COM_A4   0.056  0.023   0.014    0.008    0.008
## 846      Im4 ~~     Im21   0.055  0.005   0.005    0.018    0.018
## 847     FOOD =~     Im22   0.054  0.014   0.011    0.007    0.007
## 848      Im5 ~~   COM_A3   0.054 -0.010  -0.010   -0.012   -0.012
## 849     Im16 ~~     Im17   0.053 -0.006  -0.006   -0.025   -0.025
## 850      Im7 ~~    SAT_1   0.052  0.005   0.005    0.026    0.026
## 851     DECO  ~      Im8   0.051  0.009   0.007    0.008    0.007
## 852   CHOICE =~    SAT_3   0.051  0.009   0.012    0.010    0.010
## 853     Im13 ~~    C_CR4   0.050  0.010   0.010    0.014    0.014
## 854      Im3 ~~     Im13   0.048  0.004   0.004    0.014    0.014
## 855 PRODQUAL =~   C_REP1   0.048  0.007   0.005    0.007    0.007
## 856      COI =~     Im17   0.047  0.004   0.007    0.005    0.005
## 857   C_REP1 ~~    C_CR4   0.047 -0.006  -0.006   -0.012   -0.012
## 858      Im6 ~~    SAT_2   0.046 -0.005  -0.005   -0.012   -0.012
## 859    C_CR3 ~~    C_CR4   0.045 -0.051  -0.051   -0.037   -0.037
## 860     Im13 ~~   C_REP3   0.045  0.003   0.003    0.012    0.012
## 861     Im18 ~~    C_CR3   0.044 -0.010  -0.010   -0.012   -0.012
## 862     Im16 ~~   C_REP2   0.044  0.003   0.003    0.017    0.017
## 863      Im3 ~~    C_CR3   0.042 -0.007  -0.007   -0.013   -0.013
## 864      COI =~     Im22   0.041 -0.006  -0.010   -0.006   -0.006
## 865     Im19 ~~    C_CR3   0.041  0.009   0.009    0.013    0.013
## 866     Im20 ~~     Im16   0.041  0.007   0.007    0.012    0.012
## 867 PRODQUAL  ~      SAT   0.041 -0.010  -0.012   -0.012   -0.012
## 868 PRODQUAL ~~      SAT   0.041 -0.004  -0.009   -0.009   -0.009
## 869    C_CR1 ~~    C_CR4   0.039 -0.047  -0.047   -0.038   -0.038
## 870    BRAND =~    C_CR3   0.039 -0.010  -0.012   -0.006   -0.006
## 871    SAT_2 ~~   C_REP2   0.039  0.002   0.002    0.017    0.017
## 872     Im12 ~~     Im18   0.038 -0.005  -0.005   -0.012   -0.012
## 873     Im18 ~~   COM_A4   0.038 -0.007  -0.007   -0.011   -0.011
## 874    SAT_3 ~~   C_REP1   0.037 -0.004  -0.004   -0.010   -0.010
## 875      Im2 ~~   COM_A2   0.036 -0.005  -0.005   -0.010   -0.010
## 876    BRAND ~~      SAT   0.036  0.006   0.008    0.008    0.008
## 877   CHOICE =~   COM_A2   0.035 -0.007  -0.009   -0.006   -0.006
## 878       RI =~    C_CR4   0.033  0.020   0.012    0.006    0.006
## 879     DECO =~     Im21   0.033 -0.007  -0.009   -0.007   -0.007
## 880    BRAND =~     Im21   0.032 -0.008  -0.010   -0.007   -0.007
## 881      Im3 ~~      Im6   0.032  0.003   0.003    0.010    0.010
## 882      Im1 ~~    C_CR4   0.031 -0.006  -0.006   -0.020   -0.020
## 883     DECO =~     Im10   0.030 -0.004  -0.004   -0.005   -0.005
## 884     DECO =~     Im14   0.030  0.004   0.004    0.005    0.005
## 885     Im21 ~~     Im19   0.029 -0.005  -0.005   -0.010   -0.010
## 886     Im11 ~~    C_CR3   0.029  0.010   0.010    0.009    0.009
## 887    ATMOS =~      Im7   0.027  0.007   0.008    0.007    0.007
## 888    ATMOS =~      Im6   0.027 -0.006  -0.007   -0.006   -0.006
## 889    ATMOS =~    SAT_3   0.027 -0.006  -0.008   -0.007   -0.007
## 890     Im11 ~~    SAT_3   0.023 -0.006  -0.006   -0.008   -0.008
## 891     FOOD =~   COM_A4   0.023 -0.009  -0.008   -0.004   -0.004
## 892       RI =~    C_CR3   0.021  0.016   0.010    0.005    0.005
## 893      Im5 ~~     Im13   0.021 -0.004  -0.004   -0.008   -0.008
## 894     FOOD =~     Im18   0.021 -0.007  -0.006   -0.004   -0.004
## 895     FOOD =~     Im17   0.021  0.007   0.006    0.005    0.005
## 896      Im2 ~~    C_CR3   0.019  0.005   0.005    0.008    0.008
## 897      COI =~     Im19   0.017  0.003   0.005    0.004    0.004
## 898      SAT =~      Im7   0.017 -0.006  -0.005   -0.004   -0.004
## 899   CHOICE  ~      Im9   0.016 -0.004  -0.003   -0.004   -0.003
## 900   C_REP1 ~~    C_CR1   0.016 -0.003  -0.003   -0.008   -0.008
## 901     Im21 ~~      Im6   0.016 -0.004  -0.004   -0.007   -0.007
## 902    SAT_1 ~~    SAT_2   0.016  0.007   0.007    0.023    0.023
## 903      Im6 ~~   COM_A4   0.016 -0.005  -0.005   -0.007   -0.007
## 904     Im21 ~~    SAT_1   0.015  0.003   0.003    0.008    0.008
## 905    AFCOM =~      Im3   0.015  0.003   0.003    0.003    0.003
## 906      COI =~    SAT_1   0.015  0.002   0.004    0.004    0.004
## 907      Im2 ~~    SAT_3   0.014 -0.003  -0.003   -0.006   -0.006
## 908      COI =~   COM_A2   0.014  0.004   0.006    0.004    0.004
## 909 PRODQUAL  ~      Im8   0.014  0.003   0.004    0.004    0.004
## 910     DECO =~   COM_A1   0.014 -0.004  -0.005   -0.004   -0.004
## 911      Im1 ~~      Im7   0.013 -0.002  -0.002   -0.024   -0.024
## 912     PROF =~     Im14   0.012 -0.004  -0.004   -0.004   -0.004
## 913     PROF =~     Im10   0.012  0.004   0.004    0.004    0.004
## 914       RI =~    SAT_3   0.012 -0.009  -0.005   -0.005   -0.005
## 915      Im3 ~~     Im21   0.012 -0.002  -0.002   -0.006   -0.006
## 916     Im20 ~~    C_CR4   0.012  0.006   0.006    0.006    0.006
## 917      Im4 ~~     Im13   0.010 -0.002  -0.002   -0.009   -0.009
## 918 PRODQUAL =~      Im3   0.010  0.005   0.003    0.002    0.002
## 919      Im5 ~~    C_CR1   0.010  0.005   0.005    0.006    0.006
## 920     DECO =~    C_CR3   0.010  0.005   0.006    0.003    0.003
## 921   CHOICE =~      Im7   0.010  0.003   0.004    0.004    0.004
## 922      Im6 ~~    C_CR3   0.009 -0.004  -0.004   -0.005   -0.005
## 923      COI =~     Im10   0.009  0.001   0.002    0.002    0.002
## 924    BRAND ~~    AFCOM   0.008 -0.004  -0.003   -0.003   -0.003
## 925   COM_A4 ~~    C_CR1   0.008 -0.005  -0.005   -0.006   -0.006
## 926      Im4 ~~    SAT_3   0.007  0.002   0.002    0.007    0.007
## 927     Im14 ~~     Im19   0.007  0.001   0.001    0.007    0.007
## 928       RI  ~     DECO   0.007  0.002   0.004    0.004    0.004
## 929   FRENCH =~     Im19   0.007  0.004   0.004    0.004    0.004
## 930   CHOICE ~~      COI   0.007 -0.006  -0.003   -0.003   -0.003
## 931       RI =~     Im19   0.006  0.005   0.003    0.003    0.003
## 932   CHOICE  ~       RI   0.006 -0.007  -0.003   -0.003   -0.003
## 933      Im1 ~~     Im19   0.006 -0.002  -0.002   -0.010   -0.010
## 934     Im16 ~~      Im6   0.006 -0.002  -0.002   -0.004   -0.004
## 935      Im1 ~~   C_REP1   0.005 -0.001  -0.001   -0.008   -0.008
## 936     PROF =~   C_REP2   0.005 -0.002  -0.001   -0.002   -0.002
## 937      Im5 ~~   C_REP3   0.004 -0.001  -0.001   -0.003   -0.003
## 938     Im19 ~~    C_CR4   0.004 -0.003  -0.003   -0.004   -0.004
## 939     Im19 ~~    C_CR1   0.004 -0.003  -0.003   -0.004   -0.004
## 940     Im18 ~~   COM_A3   0.004  0.002   0.002    0.003    0.003
## 941     Im22 ~~    C_CR4   0.004 -0.003  -0.003   -0.004   -0.004
## 942     Im11 ~~   C_REP3   0.003  0.001   0.001    0.003    0.003
## 943     FOOD =~     Im12   0.003  0.003   0.002    0.002    0.002
## 944   COM_A3 ~~    C_CR4   0.003  0.004   0.004    0.003    0.003
## 945      COI  ~       RI   0.003  0.064   0.023    0.023    0.023
## 946     Im12 ~~     Im19   0.003 -0.001  -0.001   -0.004   -0.004
## 947 PRODQUAL =~    C_CR3   0.003 -0.005  -0.003   -0.002   -0.002
## 948    BRAND ~~       RI   0.002  0.001   0.002    0.002    0.002
## 949     Im13 ~~    C_CR1   0.002 -0.002  -0.002   -0.003   -0.003
## 950     Im16 ~~   COM_A2   0.001  0.002   0.002    0.002    0.002
## 951   FRENCH =~     Im12   0.001 -0.002  -0.002   -0.001   -0.001
## 952     Im12 ~~      Im1   0.001  0.001   0.001    0.004    0.004
## 953    BRAND =~   COM_A1   0.001 -0.001  -0.001   -0.001   -0.001
## 954      Im3 ~~     Im16   0.001  0.001   0.001    0.001    0.001
## 955   FRENCH =~      Im4   0.000  0.001   0.001    0.000    0.000
## 956     PROF =~   COM_A4   0.000 -0.001  -0.001   -0.001   -0.001
## 957     DECO =~     Im19   0.000  0.001   0.002    0.001    0.001
## 958     DECO =~     Im16   0.000 -0.001  -0.002   -0.001   -0.001
## 959     Im21 ~~   C_REP2   0.000  0.000   0.000   -0.001   -0.001
## 960      COI =~     Im20   0.000  0.000  -0.001    0.000    0.000
## 961     Im18 ~~    SAT_3   0.000  0.000   0.000    0.000    0.000
## 962    ATMOS  ~      COI   0.000  0.000   0.000    0.000    0.000
## 963 PRODQUAL =~    SAT_3   0.000  0.000   0.000    0.000    0.000
## 964      COI =~     Im18   0.000  0.000   0.000    0.000    0.000
## 965     Im10 ~~     Im22   0.000  0.000   0.000    0.000    0.000
## 966     DECO  ~       RI   0.000  0.000   0.000    0.000    0.000